Textbook QuestionUse the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>f(−1)24views
Textbook QuestionUse the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>lim x→−1^− f(x)29views
Textbook QuestionUse the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>lim x→−1^+ f(x)28views
Textbook QuestionUse the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>lim x→−1 f(x)22views
Textbook QuestionUse the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>f(1)28views
Textbook QuestionUse the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>lim x→1 f(x)31views
Textbook QuestionUse the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>lim x→3^− f(x)27views
Textbook QuestionUse the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>lim x→3^+ f(x)21views
Textbook QuestionUse the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>lim x→3 f(x)25views
Textbook QuestionThe following table gives the position s(t)s\left(t\right)s(t) of an object moving along a line at time ttt. Determine the average velocities over the time intervals [1,1.01]\left\lbrack1,1.01\right\rbrack[1,1.01], [1,1.001]\left\lbrack1,1.001\right\rbrack[1,1.001], and [1,1.0001]\left\lbrack1,1.0001^{}\right.][1,1.0001]. Then make a conjecture about the value of the instantaneous velocity at t=1t=1t=1. <IMAGE>29views
Textbook QuestionGiven the function f(x)=−16x2+64xf\left(x\right)=-16x^2+64xf(x)=−16x2+64x, complete the following. <IMAGE>Find the slopes of the secant lines that pass though the points (x,f(x))\left(x,f\left(x\right)\right)(x,f(x)) and (2,f(2))\left(2,f\left(2\right)\right)(2,f(2)), for x=1.5,1.9,1.99,1.999,x=1.5,1.9,1.99,1.999,x=1.5,1.9,1.99,1.999, and 1.99991.99991.9999 (see figure).32views
Textbook QuestionGiven the function f(x)=−16x2+64xf\left(x\right)=-16x^2+64xf(x)=−16x2+64x, complete the following. <IMAGE>Make a conjecture about the value of the limit of the slopes of the secant lines that pass through (x,f(x))\left(x,f\left(x\right)\right)(x,f(x)) and (2,f(2))\left(2,f\left(2\right)\right)(2,f(2)) as xxx approaches 222.32views
Textbook QuestionThe position of an object moving vertically along a line is given by the function s(t)=−16t2+128ts\left(t\right)=-16t^2+128ts(t)=−16t2+128t. Find the average velocity of the object over the following intervals.[1,4]\left\lbrack1,4\right\rbrack[1,4]28views
Textbook QuestionThe position of an object moving vertically along a line is given by the function s(t)=−16t2+128ts\left(t\right)=-16t^2+128ts(t)=−16t2+128t. Find the average velocity of the object over the following intervals.[1,2]\left\lbrack1,2\right\rbrack[1,2]35views
Textbook QuestionThe position of an object moving vertically along a line is given by the function s(t)=−4.9t2+30t+20s\left(t\right)=-4.9t^2+30t+20s(t)=−4.9t2+30t+20. Find the average velocity of the object over the following intervals.[0,3]\left\lbrack0,3\right\rbrack[0,3]32views
Textbook QuestionThe position of an object moving vertically along a line is given by the function s(t)=−4.9t2+30t+20s\left(t\right)=-4.9t^2+30t+20s(t)=−4.9t2+30t+20. Find the average velocity of the object over the following intervals.[0,h]\left\lbrack0,h\right\rbrack[0,h], where h>0h\gt{0}h>0 is a real number36views
Textbook QuestionUse the graph of f in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. <IMAGE>limx→1−f(x)\lim_{x\to1^{-}}f\left(x\right) 35views
Textbook QuestionUse the graph of f in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. <IMAGE>limx→1+f(x)\lim_{x\to1^{+}}f\left(x\right) 27views
Textbook QuestionUse the graph of f in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. <IMAGE>a. f(1)35views
Textbook QuestionUse the graph of f in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. <IMAGE>d. limx→1f(x)\lim_{x\to1}f\left(x\right) 22views
Textbook QuestionUse the graph of f in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. <IMAGE>h. limx→3f(x)\lim_{x\to3}f\left(x\right) 36views
Textbook QuestionUse the graph of f in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. <IMAGE>l. limx→2f(x)\lim_{x\to2}f\left(x\right) 46views
Textbook QuestionConsider the position function s(t) =−16t^2+100t representing the position of an object moving vertically along a line. Sketch a graph of s with the secant line passing through (0.5, s(0.5)) and (2, s(2)). Determine the slope of the secant line and explain its relationship to the moving object.10views
Textbook QuestionConsider the position function s(t)=−16t^2+128t (Exercise 13). Complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t=1. <IMAGE>27views
Textbook QuestionConsider the position function s(t)=−16t^2+100t. Complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t=3. <IMAGE>25views
Textbook QuestionUse the graph of hhh in the figure to find the following values or state that they do not exist. <IMAGE>h(2)h\left(2\right)h(2)26views
Textbook QuestionUse the graph of hhh in the figure to find the following values or state that they do not exist. <IMAGE>limx→4h(x){\displaystyle\lim_{x\to4}h\left(x\right)}x→4limh(x)27views
Textbook QuestionUse the graph of g(x)g(x) in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. <IMAGE>limx→2g(x)\lim_{x\to2}g\left(x\right)limx→2g(x)30views
Textbook QuestionUse the graph of g(x) in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. <IMAGE>limx→4g(x)\lim_{x\to4}g\left(x\right) 23views
Textbook QuestionUse the graph of ggg in the figure to find the following values or state that they do not exist. <IMAGE>limx→0g(x){\displaystyle\lim_{x\to0}g\left(x\right)}x→0limg(x)22views
Textbook QuestionUse the graph of fff in the figure to find the following values or state that they do not exist. <IMAGE>f(1)f\left(1\right)f(1)26views
Textbook QuestionUse the graph of fff in the figure to find the following values or state that they do not exist. <IMAGE>f(0)f\left(0\right)f(0)25views
Textbook QuestionLet f(x)=x2−4x−2f\left(x\right)=\frac{x^2-4}{x-2}f(x)=x−2x2−4 . <IMAGE>Calculate f(x)f\left(x\right)f(x) for each value of xxx in the following table.28views
Textbook QuestionLet f(x)=x2−4x−2f\left(x\right)=\frac{x^2-4}{x-2}f(x)=x−2x2−4. <IMAGE>Make a conjecture about the value of limx→2x2−4x−2{\displaystyle\lim_{x\to2}\frac{x^2-4}{x-2}}x→2limx−2x2−4.30views
Textbook QuestionThe function s(t)s(t)s(t) represents the position of an object at time t moving along a line. Suppose s(2)=136s(2)=136s(2)=136 and s(3)=156s(3)=156s(3)=156 . Find the average velocity of the object over the interval of time [2,3][2, 3][2,3] .22views
Textbook QuestionThe table gives the position s(t)of an object moving along a line at time t, over a two-second interval. Find the average velocity of the object over the following intervals. <IMAGE>a. [0,2][0, 2][0,2]32views
Textbook QuestionThe table gives the position s(t)of an object moving along a line at time t, over a two-second interval. Find the average velocity of the object over the following intervals. <IMAGE>c. [0,1][0, 1][0,1]24views
Textbook QuestionFor the following position functions, make a table of average velocities similar to those in Exercises 19–20 and make a conjecture about the instantaneous velocity at the indicated time. a. s(t)=−16t^2+80t+60 at t=329views
Textbook QuestionFor the following position functions, make a table of average velocities similar to those in Exercises 19–20 and make a conjecture about the instantaneous velocity at the indicated time. c. s(t)=40 sin 2t at t=025views
Textbook QuestionA projectile is fired vertically upward and has a position given by s(t)=−16t^2+128t+192, for 0≤t≤9.a. Graph the position function, for 0≤t≤9.11views
Textbook QuestionA projectile is fired vertically upward and has a position given by s(t)=−16t^2+128t+192, for 0≤t≤9.b. From the graph of the position function, identify the time at which the projectile has an instantaneous velocity of zero; call this time t=a.26views
Textbook QuestionA projectile is fired vertically upward and has a position given by s(t)=−16t^2+128t+192, for 0≤t≤9.d. For what values of t on the interval [0, 9] is the instantaneous velocity positive (the projectile moves upward)?29views
Textbook QuestionA rock is dropped off the edge of a cliff, and its distance s (in feet) from the top of the cliff after t seconds is s(t)=16t^2. Assume the distance from the top of the cliff to the ground is 96 ft.a. When will the rock strike the ground? 30views
Textbook QuestionLet g(t)=t−9t−3g\left(t\right)=\frac{t-9}{\sqrt{t}-3}g(t)=t−3t−9.Make two tables, one showing values of ggg for t=8.9,8.99t=8.9,8.99t=8.9,8.99, and 8.9998.9998.999 and one showing values of ggg for t=9.1,9.01t=9.1,9.01t=9.1,9.01, and 9.0019.0019.001.24views
Textbook QuestionLet g(t)=t−9t−3g\left(t\right)=\frac{t-9}{\sqrt{t}-3}g(t)=t−3t−9.Make a conjecture about the value of limt→9t−9t−3{\displaystyle\lim_{t\to9}\frac{t-9}{\sqrt{t}-3}}t→9limt−3t−9.28views
Textbook QuestionLet g(x)=x3−4x8∣x−2∣g\left(x\right)=\frac{x^3-4x}{8\left|x-2\right|}g(x)=8∣x−2∣x3−4x. <IMAGE>Calculate g(x)g\left(x\right)g(x) for each value of xxx in the following table.26views
Textbook QuestionLet g(x)=x3−4x8∣x−2∣g\left(x\right)=\frac{x^3-4x}{8\left|x-2\right|}g(x)=8∣x−2∣x3−4x. <IMAGE>Make a conjecture about the values of limx→2−g(x){\displaystyle\lim_{x\to2^{-}}g\left(x\right)}x→2−limg(x), limx→2+g(x){\displaystyle\lim_{x\to2^{+}}g\left(x\right)}x→2+limg(x), and limx→2g(x){\displaystyle\lim_{x\to2}g\left(x\right)}x→2limg(x) or state that they do not exist.29views
Textbook QuestionUse a graph of f to estimate limx→af(x){\displaystyle\lim_{x\to a}f\left(x\right)} or to show that the limit does not exist. Evaluate f(x) near x=ax=a to support your conjecture.f(x)=x−2ln∣x−2∣f\left(x\right)=\frac{x-2}{\ln\left|x-2\right|}; a=2a=2 26views
Textbook QuestionUse a graph of f to estimate limx→af(x){\displaystyle\lim_{x\to a}}f\left(x\right) or to show that the limit does not exist. Evaluate f(x) near x=ax=a to support your conjecture.f(x)=1−cos(2x−2)(x−1)2;a=1f\left(x\right)=\frac{1-\cos\left(2x-2\right)}{\left(x-1\right)^2};a=1 29views
Textbook QuestionDetermine whether the following statements are true and give an explanation or counterexample.a. The value of limx→3x2−9x−3{\displaystyle\lim_{x\to3}}\frac{x^2-9}{x-3} does not exist.31views
Textbook QuestionDetermine whether the following statements are true and give an explanation or counterexample.d. limx→0x{\displaystyle\lim_{x\to0}}\sqrt{x} . (Hint: Graph y=√x)31views
Textbook QuestionDetermine whether the following statements are true and give an explanation or counterexample.e. limx→π2cotx=0{\displaystyle\lim_{x\to\frac{\pi}{2}}}\cot x=0 . (Hint: Graph y=cot x)24views
Textbook QuestionSketch the graph of a function with the given properties. You do not need to find a formula for the function. f(2) = 1,lim x→2 f(x) = 327views
Textbook QuestionSketch the graph of a function with the given properties. You do not need to find a formula for the function. p(0) = 2,lim x→0 p(x) = 0,lim x→2 p(x) does not exist, p(2)=lim x→2^+ p(x)=112views
Textbook QuestionFor any real number x, the floor function (or greatest integer function) ⌊x⌋ is the greatest integer less than or equal to x (see figure).a. Compute lim x→−1^− ⌊x⌋, lim x→−1^+ ⌊x⌋,lim x→2^− ⌊x⌋, and lim x→2^+ ⌊x⌋.26views
Textbook QuestionA function f is even if f(−x)=f(x), for all x in the domain of f. Suppose f is even, with lim x→2^+ f(x)=5 and lim x→2^− f(x)=8. Evaluate the following limits.a. lim x→−2^+ f(x)26views
Textbook QuestionEstimate the following limits using graphs or tables.limh→0ln(1+h)h{\displaystyle\lim_{h\to0}}\frac{\ln\left(1+h\right)}{h} 27views
Textbook QuestionEstimate the following limits using graphs or tables.lim x→1 9(√2x − x^4 −3√x) / 1 − x^3/420views
Textbook QuestionDetermine limx→∞f(x)\lim_{x\rightarrow\infty}f\left(x\right) and limx→−∞f(x)\lim_{x\rightarrow-\infty}f\left(x\right) for the following functions. Then give the horizontal asymptotes of ff (if any).f(x)=4x20x+1f\left(x\right)=\frac{4x}{20x+1}27views
Textbook QuestionDetermine limx→∞f(x)\lim_{x\rightarrow\infty}f\left(x\right)limx→∞f(x) and limx→−∞f(x)\lim_{x\rightarrow-\infty}f\left(x\right)limx→−∞f(x) for the following functions. Then give the horizontal asymptotes of fff (if any).f(x)=6x2−9x+83x2+2f\left(x\right)=\frac{6x^2-9x+8}{3x^2+2} 25views
Textbook QuestionDetermine limx→∞f(x)\lim_{x\rightarrow\infty}f\left(x\right)limx→∞f(x) and limx→−∞f(x)\lim_{x\rightarrow-\infty}f\left(x\right)limx→−∞f(x) for the following functions. Then give the horizontal asymptotes of fff (if any).f(x)=3x3−7x4+5x2f\left(x\right)=\frac{3x^3-7}{x^4+5x^2} 22views
Textbook QuestionDetermine limx→∞f(x)\lim_{x\rightarrow\infty}f\left(x\right)limx→∞f(x) and limx→−∞f(x)\lim_{x\rightarrow-\infty}f\left(x\right)limx→−∞f(x) for the following functions. Then give the horizontal asymptotes of fff (if any).f(x)=40x5+x216x4−2xf\left(x\right)=\frac{40x^5+x^2}{16x^4-2x} 26views
Textbook QuestionDetermine limx→∞f(x)\lim_{x\rightarrow\infty}f\left(x\right)limx→∞f(x) and limx→−∞f(x)\lim_{x\rightarrow-\infty}f\left(x\right)limx→−∞f(x) for the following functions. Then give the horizontal asymptotes of fff (if any).f(x)=12x4−4x8−9x4f\left(x\right)=\frac{1}{2x^4-\sqrt{4x^8-9x^4}} 31views
Textbook QuestionDetermine limx→∞f(x)\lim_{x\rightarrow\infty}f\left(x\right)limx→∞f(x) and limx→−∞f(x)\lim_{x\rightarrow-\infty}f\left(x\right)limx→−∞f(x) for the following functions. Then give the horizontal asymptotes of fff (if any).f(x)=4x3+12x3+16x6+1f\left(x\right)=\frac{4x^3+1}{2x^3+\sqrt{16x^6+1}} 30views
Textbook QuestionDetermine limx→∞f(x)\lim_{x\rightarrow\infty}f\left(x\right)limx→∞f(x) and limx→−∞f(x)\lim_{x\rightarrow-\infty}f\left(x\right)limx→−∞f(x) for the following functions. Then give the horizontal asymptotes of fff (if any).f(x)=x6+834x2+3x4+1f\left(x\right)=\frac{\sqrt[3]{x^6+8}}{4x^2+\sqrt{3x^4+1}} 26views
Textbook QuestionDetermine limx→∞f(x)\lim_{x\rightarrow\infty}f\left(x\right)limx→∞f(x) and limx→−∞f(x)\lim_{x\rightarrow-\infty}f\left(x\right)limx→−∞f(x) for the following functions. Then give the horizontal asymptotes of fff (if any).f(x)=4x(3x−9x2+1)f\left(x\right)=4x\left(3x-\sqrt{9x^2+1}\right) 30views
Textbook QuestionComplete the following steps for the given functions. b. Find the vertical asymptotes of ff (if any).f(x)=x2−3x+6f\left(x\right)=\frac{x^2-3}{x+6}30views
Textbook QuestionComplete the following steps for the given functions. a. Find the slant asymptote of ff.f(x)=x2−2x+53x−2f\left(x\right)=\frac{x^2-2x+5}{3x-2}17views
Textbook QuestionComplete the following steps for the given functions. b. Find the vertical asymptotes of ff (if any).f(x)=x2−2x+53x−2f\left(x\right)=\frac{x^2-2x+5}{3x-2} 27views
Textbook QuestionComplete the following steps for the given functions. a. Find the slant asymptote of ff.f(x)=4x3+4x2+7x+4x2+1f\left(x\right)=\frac{4x^3+4x^2+7x+4}{x^2+1} 26views
Textbook QuestionComplete the following steps for the given functions. b. Find the vertical asymptotes of fff (if any).f(x)=4x3+4x2+7x+4x2+1f\left(x\right)=\frac{4x^3+4x^2+7x+4}{x^2+1}f(x)=x2+14x3+4x2+7x+4 26views
Textbook QuestionComplete the following steps for the given functions. a. Find the slant asymptote of ff.f(x)=3x2−2x+53x+4f\left(x\right)=\frac{3x^2-2x+5}{3x+4}29views
Textbook QuestionComplete the following steps for the given functions. b. Find the vertical asymptotes of f (if any).f(x)=3x2−2x+53x+4f\left(x\right)=\frac{3x^2-2x+5}{3x+4}28views
Textbook QuestionDetermine the end behavior of the following transcendental functions by analyzing appropriate limits. Then provide a simple sketch of the associated graph, showing asymptotes if they exist. f(x)=−3e−xf\left(x\right)=-3e^{-x}22views
Textbook QuestionDetermine the end behavior of the following transcendental functions by analyzing appropriate limits. Then provide a simple sketch of the associated graph, showing asymptotes if they exist. f(x)=1−lnxf\left(x\right)=1-\ln x25views
Textbook QuestionDetermine the end behavior of the following transcendental functions by analyzing appropriate limits. Then provide a simple sketch of the associated graph, showing asymptotes if they exist. f(x)=sinxf\left(x\right)=\sin x9views
Textbook QuestionUse an appropriate limit definition to prove the following limits.lim x→1 (5x−2) =3;26views
Textbook QuestionUse an appropriate limit definition to prove the following limits.lim x→ 5x^2 − 25 / x − 5=1024views
Textbook QuestionDetermine whether the following statements are true and give an explanation or counterexample.a. The graph of a function can never cross one of its horizontal asymptotes.28views
Textbook QuestionDetermine whether the following statements are true and give an explanation or counterexample.c. The graph of a function can have any number of vertical asymptotes but at most two horizontal asymptotes.26views
Textbook QuestionIf a function f represents a system that varies in time, the existence of lim limt→∞f(t){\displaystyle\lim_{t\rightarrow\infty}{f(t)}} means that the system reaches a steady state (or equilibrium). For the following systems, determine whether a steady state exists and give the steady-state value.The population of a bacteria culture is given by p(t)=2500t+1p\left(t\right)=\frac{2500}{t+1}.30views
Textbook QuestionIf a function f represents a system that varies in time, the existence of lim limt→∞f(t){\displaystyle\lim_{t\rightarrow\infty}{f(t)}}t→∞limf(t) means that the system reaches a steady state (or equilibrium). For the following systems, determine whether a steady state exists and give the steady-state value.The population of a culture of tumor cells is given by p(t)=3500tt+1p\left(t\right)=\frac{3500t}{t+1}.20views
Textbook QuestionIf a function f represents a system that varies in time, the existence of lim limt→∞f(t){\displaystyle\lim_{t\rightarrow\infty}{f(t)}}t→∞limf(t) means that the system reaches a steady state (or equilibrium). For the following systems, determine whether a steady state exists and give the steady-state value.The population of a colony of squirrels is given by p(t)=15003+2e−0.1tp\left(t\right)=\frac{1500}{3+2e^{-0.1t}}.26views
Textbook QuestionThe hyperbolic cosine function, denoted cosh(x)\cosh\left(x\right)cosh(x), is used to model the shape of a hanging cable (a telephone wire, for example). It is defined as cosh(x)=ex+e−x2\cosh\left(x\right)=\frac{e^{x}+e^{-x}}{2}cosh(x)=2ex+e−x.b. Evaluate cosh(0)\cosh\left(0\right). Use symmetry and part (a) to sketch a plausible graph for y=cosh(x)y=\cosh\left(x\right).25views
Textbook QuestionConsider the graph of y=cot^−1 x(see Section 1.4) and determine the following limits using the graph.lim x→∞ cot^−1 23views
Textbook QuestionConsider the graph of y=cot^−1 x(see Section 1.4) and determine the following limits using the graph.lim x→−∞ cot^−1x7views
Textbook QuestionDetermine the following limits at infinity.lim t→∞ et,lim t→−∞ e^t,and lim t→∞ e^−t27views
Textbook QuestionSketch a possible graph of a function f that satisfies all of the given conditions. Be sure to identify all vertical and horizontal asymptotes.f(−1)=−2f\left(-1\right)=-2, f(1)=2f\left(1\right)=2, f(0)=0f\left(0\right)=0, limx→∞f(x)=1{\displaystyle\lim_{x\to\infty}{f(x)=1}}, limx→−∞f(x)=−1{\displaystyle\lim_{x\to-\infty}{f(x)=-1}}13views
Textbook Questiona. Estimate lim x→π/4 cos 2x / cos x − sin x by making a table of values of cos 2x / cos x − sin x for values of x approaching π/4. Round your estimate to four digits.23views
Textbook QuestionSketch a graph of f and use it to make a conjecture about the values of f(a), lim x→a^−f(x),lim x→a^+f(x), and lim x→a f(x) or state that they do not exist.f(x) = {x^2+1 if x≤−13 if x>−1; a=−18views
Textbook QuestionSketch a graph of f and use it to make a conjecture about the values of f(a), lim x→a^−f(x),lim x→a^+f(x), and lim x→a f(x) or state that they do not exist.f(x) = {√x if x<43 if x=4; a=4x+1 if x>46views
Textbook QuestionSketch a graph of f and use it to make a conjecture about the values of f(a), lim x→a^−f(x),lim x→a^+f(x), and lim x→a f(x) or state that they do not exist.f(x) = x^2−25 / x−5; a=510views
Textbook QuestionSketch a graph of f and use it to make a conjecture about the values of f(a), lim x→a^−f(x),lim x→a^+f(x), and lim x→a f(x) or state that they do not exist.f(x) = x^2+x−2 / x−1; a=122views
Textbook QuestionA function f is even if f(−x)=f(x), for all x in the domain of f. Suppose f is even, with lim x→2^+ f(x)=5 and lim x→2^− f(x)=8. Evaluate the following limits.lim x→−2^− f(x)24views
Textbook QuestionPostage rates Assume postage for sending a first-class letter in the United States is $0.47 for the first ounce (up to and including 1 oz) plus $0.21 for each additional ounce (up to and including each additional ounce).a. Graph the function p=f(w) that gives the postage p for sending a letter that weighs w ounces, for 0<w≤3.5.8views
Textbook QuestionAnalyze the following limits. Then sketch a graph of y=tanx with the window [−π,π]×[−10,10]and use your graph to check your work.lim x→π/2^+ tan x7views
Textbook QuestionAnalyze the following limits. Then sketch a graph of y=tanx with the window [−π,π]×[−10,10]and use your graph to check your work.lim x→π/2^− tan x13views
Textbook QuestionAnalyze the following limits. Then sketch a graph of y=tanx with the window [−π,π]×[−10,10]and use your graph to check your work.lim x→π/2^+ tan x9views
Textbook QuestionAnalyze the following limits. Then sketch a graph of y=tanx with the window [−π,π]×[−10,10]and use your graph to check your work.lim x→π/2^− tan x11views
Textbook QuestionFind polynomials p and q such that f=p/q is undefined at 1 and 2, but f has a vertical asymptote only at 2. Sketch a graph of your function.14views
Textbook QuestionDetermine whether the following statements are true and give an explanation or counterexample.The line x=−1 is a vertical asymptote of the function f(x) =x^2 − 7x + 6 / x^2 − 1.6views
Textbook QuestionUse analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions.f(x)=x^2−3x+2 / x^10−x^99views
Textbook QuestionUse analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions.h(x)=e^x(x+1)^310views
Textbook QuestionUse analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions.g(θ)=tan πθ/107views
Textbook QuestionUse analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions.f(x)=1/ √x sec x12views
Textbook QuestionSuppose f(x) lies in the interval (2, 6). What is the smallest value of ε such that |f (x)−4|<ε?22views
Textbook QuestionWhich one of the following intervals is not symmetric about x=5?a.(1, 9)b.(4, 6)c.(3, 8)d.(4.5, 5.5)23views
Textbook QuestionSuppose |f(x) − 5|<0.1 whenever 0<x<5. Find all values of δ>0 such that |f(x) − 5|<0.1 whenever 0<|x−2|<δ.12views
Textbook QuestionUse the precise definition of a limit to prove the following limits. Specify a relationship between ε and δ that guarantees the limit exists.lim x→1 (8x+5)=139views
Textbook QuestionUse the precise definition of a limit to prove the following limits. Specify a relationship between ε and δ that guarantees the limit exists.lim x→4 x^2−16 / x−4=8 (Hint: Factor and simplify.)16views
Textbook QuestionUse the precise definition of a limit to prove the following limits. Specify a relationship between ε and δ that guarantees the limit exists.lim x→7 f(x)=9, where f(x)={3x−12 if x≤7x+2 if x>734views
Textbook QuestionUse the precise definition of a limit to prove the following limits. Specify a relationship between ε and δ that guarantees the limit exists.lim x→0 x^2=0 (Hint: Use the identity √x2=|x|.)18views
Textbook QuestionUse the precise definition of a limit to prove the following limits. Specify a relationship between ε and δ that guarantees the limit exists.lim x→2 (x^2+3x)=1012views
Textbook QuestionUse the precise definition of a limit to prove the following limits. Specify a relationship between ε and δ that guarantees the limit exists.lim x→−3 |2x|=6 (Hint: Use the inequality ∥a|−|b∥≤|a−b|, which holds for all constants a and b (see Exercise 74).)18views
Textbook QuestionUse the precise definition of a limit to prove the following limits. Specify a relationship between ε and δ that guarantees the limit exists.lim x→a (mx+b)=ma+b, for any constants a, b, and m15views
Textbook QuestionUse the precise definition of a limit to prove the following limits. Specify a relationship between ε and δ that guarantees the limit exists.lim x→3 x^3=2715views
Textbook QuestionUse the precise definition of a limit to prove the following limits. Specify a relationship between ε and δ that guarantees the limit exists.lim x→1 x^4=110views
Textbook QuestionUse the precise definition of a limit to prove the following limits. Specify a relationship between ε and δ that guarantees the limit exists.lim x→5 1/x^2=1/2515views
Textbook QuestionDetermine the following limits.Assume the function g satisfies the inequality 1≤g(x) ≤sin^2 x + 1, for all values of x near 0. Find lim x→0 g(x).8views
Textbook QuestionLet f(x) =x^2−2x+3.a. For ε=0.25, find the largest value of δ>0 satisfying the statement|f(x)−2|<ε whenever 0<|x−1|<δ.13views
Textbook QuestionDetermine whether the following statements are true and give an explanation or counterexample. Assume a and L are finite numbers and assume lim x→a f(x) =Ld. If |x−a|<δ, then a−δ<x<a+δ.9views
Textbook QuestionGiven the graph of f in the following figures, find the slope of the secant line that passes through (0,0) and (h,f(h))in terms of h, for h>0 and h<0.f(x)=x1/3 <IMAGE>10views
Textbook QuestionSuppose limx→a f(x)=L{\displaystyle\lim_{x\to a}}\text{ }f\left(x\right)=L and limx→a g(x)=M{\displaystyle\lim_{x\to a}}\text{ }g\left(x\right)=M. Prove that limx→a (f(x)−g(x))=L−M{\displaystyle\lim_{x\to a}}\text{ }\left(f\left(x\right)-g\left(x\right)\right)=L-M.13views
Textbook QuestionSuppose limx→a f(x)=L{\displaystyle\lim_{x\to a}}\text{ }f\left(x\right)=Lx→alim f(x)=L. Prove that limx→a (c(f(x))=cL{\displaystyle\lim_{x\to a}}\text{ (}c\left(f\left(x\right)\right)=cL, where cc is a constant.11views
Textbook QuestionUse the precise definition of infinite limits to prove the following limits.limx→41(x−4)2=∞{\displaystyle\lim_{x\to4}}\frac{1}{\left(x-4\right)^2}=\infty7views
Textbook QuestionUse the precise definition of infinite limits to prove the following limits.limx→−11(x+1)4=∞{\displaystyle\lim_{x\to-1}}\frac{1}{\left(x+1\right)^4}=\infty 7views
Textbook QuestionUse the precise definition of infinite limits to prove the following limits.limx→0(1x2+1)=∞{\displaystyle\lim_{x\to0}}\left(\frac{1}{x^2}+1\right)=\infty9views
Textbook QuestionUse the precise definition of infinite limits to prove the following limits.limx→0(1x4−sin(x))=∞{\displaystyle\lim_{x\to0}}\left(\frac{1}{x^4}-\sin\left(x\right)\right)=\infty 7views
Multiple ChoiceFind the limit by creating a table of values.limx→0−4x+2\lim_{x\rarr0}-4x+2limx→0−4x+2123views5rank1comments
Multiple ChoiceFind the limit by creating a table of values.limx→23x2+5x+1\lim_{x\rarr2}3x^2+5x+1limx→23x2+5x+188views5rank
Multiple ChoiceFind the limit by creating a table of values.limx→1x2−4x−2\lim_{x\rarr1}\frac{x^2-4}{x-2}limx→1x−2x2−482views
Multiple ChoiceFind the limit using the graph of f(x)f\left(x\right)f(x) shown.limx→1f(x)\lim_{x\rarr1}f\left(x\right)limx→1f(x)91views
Multiple ChoiceFind the limit using the graph of f(x)f\left(x\right)f(x) shown.limx→−2f(x)\lim_{x\rarr-2}f\left(x\right)limx→−2f(x)90views4rank
Multiple ChoiceFind the limit using the graph of f(x)f\left(x\right)f(x) shown.limx→4f(x)\lim_{x\rarr4}f\left(x\right)limx→4f(x)84views1rank
Multiple ChoiceUsing the graph, find the specified limit or state that the limit does not exist (DNE).limx→−2−f(x)\lim_{x\rarr-2^{-}}f\left(x\right)limx→−2−f(x), limx→−2+f(x)\lim_{x\rarr-2^{+}}f\left(x\right)limx→−2+f(x), limx→−2f(x)\lim_{x\rarr-2^{}}f\left(x\right)limx→−2f(x)69views2rank
Multiple ChoiceUsing the graph, find the specified limit or state that the limit does not exist (DNE).limx→0−f(x)\lim_{x\rightarrow0^{-}}f\left(x\right)limx→0−f(x) , limx→0+f(x)\lim_{x\rightarrow0^{+}}f\left(x\right)limx→0+f(x), limx→0f(x)\lim_{x\rightarrow0}f\left(x\right)limx→0f(x)62views1rank
Multiple ChoiceUsing the graph, find the specified limit or state that the limit does not exist.limx→4−f(x)\lim_{x\rightarrow4^{-}}f\left(x\right)limx→4−f(x), limx→4+f(x)\lim_{x\rightarrow4^{+}}f\left(x\right)limx→4+f(x), limx→4f(x)\lim_{x\rightarrow4}f\left(x\right)limx→4f(x)61views1rank
Multiple ChoiceFind the specified limit or state that the limit does not exist by creating a table of values.f(x)=1xf\left(x\right)=\frac{1}{x}f(x)=x1limx→1−f(x)\lim_{x\rightarrow1^{-}}f\left(x\right)limx→1−f(x), limx→1+f(x)\lim_{x\rightarrow1^{+}}f\left(x\right)limx→1+f(x), limx→1f(x)\lim_{x\rightarrow1}f\left(x\right)limx→1f(x)52views
Multiple ChoiceUse the graph of f(x)f\left(x\right)f(x) to estimate the value of the limit or state that it does not exist (DNE).limx→1f(x)\lim_{x\rarr1}f\left(x\right)limx→1f(x)52views1rank
Multiple ChoiceUse the graph of f(x)f\left(x\right)f(x) to estimate the value of the limit or state that it does not exist (DNE).limx→−2f(x)\lim_{x\rarr-2}f\left(x\right)limx→−2f(x)50views1rank
Multiple ChoiceUse the graph of f(x)f\left(x\right)f(x) to estimate the value of the limit or state that it does not exist (DNE).limx→0f(x)\lim_{x\rarr0}f\left(x\right)limx→0f(x)49views3rank
Multiple ChoiceUse the graph of f(x)f\left(x\right)f(x) to estimate the value of the limit or state that it does not exist (DNE).limx→0f(x)\lim_{x\rarr0}f\left(x\right)limx→0f(x)49views1rank