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Table of contents

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0. Fundamental Concepts of Algebra3h 29m
1. Equations and inequalities3h 27m
2. Graphs43m
3. Functions & Graphs2h 17m
4. Polynomial Functions1h 54m
5. Rational Functions1h 23m
6. Exponential and Logarithmic Functions2h 28m
7. Measuring Angles39m
8. Trigonometric Functions on Right Triangles2h 5m
9. Unit Circle1h 19m
10. Graphing Trigonometric Functions1h 19m
11. Inverse Trigonometric Functions and Basic Trig Equations1h 41m
12. Trigonometric Identities 34m
13. Non-Right Triangles1h 38m
14. Vectors2h 25m
15. Polar Equations2h 5m
16. Parametric Equations1h 6m
17. Graphing Complex Numbers1h 7m
18. Systems of Equations and Matrices1h 6m
19. Conic Sections2h 36m
20. Sequences, Series & Induction1h 15m
21. Combinatorics and Probability1h 45m
22. Limits & Continuity1h 49m

22. Limits & Continuity

Introduction to Limits

22. Limits & Continuity

Introduction to Limits - Video Tutorials & Practice Problems

Next Topic: Finding Limits Algebraically

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Get a 10 bullets summary of the topic

1

concept

Finding Limits Numerically and Graphically

Video duration:

6m

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2

Problem

Problem

Find the limit by creating a table of values.
$\lim_{x\rarr0}-4x+2$

A

$-4$

B

$-2$

C

$0$

D

$2$

3

Problem

Problem

Find the limit by creating a table of values.
$\lim_{x\rarr2}3x^2+5x+1$

A

$1$

B

$10$

C

$23$

D

$21$

4

Problem

Problem

Find the limit by creating a table of values.
$\lim_{x\rarr1}\frac{x^2-4}{x-2}$

A

$0$

B

$3$

C

$-3$

D

$2$

5

Problem

Problem

Find the limit using the graph of $f\left(x\right)$ shown.
$\lim_{x\rarr1}f\left(x\right)$

A

$2$

B

$1$

C

$0$

D

Unable to determine

6

Problem

Problem

Find the limit using the graph of $f\left(x\right)$ shown.
$\lim_{x\rarr-2}f\left(x\right)$

A

$4$

B

$-2$

C

$-3$

D

Unable to determine

7

Problem

Problem

Find the limit using the graph of $f\left(x\right)$ shown.
$\lim_{x\rarr4}f\left(x\right)$

A

$2$

B

$-2$

C

$0$

D

Unable to determine

8

example

Finding Limits Numerically and Graphically Example 1

Video duration:

2m

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9

concept

One-Sided Limits

Video duration:

5m

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10

Problem

Problem

Using the graph, find the specified limit or state that the limit does not exist (DNE).
$\lim_{x\rarr-2^{-}}f\left(x\right)$ , $\lim_{x\rarr-2^{+}}f\left(x\right)$ , $\lim_{x\rarr-2^{}}f\left(x\right)$

A

$\lim_{x\rarr-2^{-}}f\left(x\right)=1$ , $\lim_{x\rarr-2^{+}}f\left(x\right)=1$ , $\lim_{x\rarr-2^{}}f\left(x\right)=1$

B

$\lim_{x\rarr-2^{-}}f\left(x\right)=1$ , $\lim_{x\rarr-2^{+}}f\left(x\right)=-1$ , $\lim_{x\rarr-2}f\left(x\right)=DNE$

C

$\lim_{x\rarr-2^{-}}f\left(x\right)=1$ , $\lim_{x\rarr-2^{+}}f\left(x\right)=1$ , $\lim_{x\rarr-2}f\left(x\right)=DNE$

D

$\lim_{x\rarr-2^{-}}f\left(x\right)=0$ , $\lim_{x\rarr-2^{+}}f\left(x\right)=0$ , $\lim_{x\rarr-2}f\left(x\right)=0$

11

Problem

Problem

Using the graph, find the specified limit or state that the limit does not exist (DNE).
$\lim_{x\rightarrow0^{-}}f\left(x\right)$ , $\lim_{x\rightarrow0^{+}}f\left(x\right)$ , $\lim_{x\rightarrow0}f\left(x\right)$

A

$\lim_{x\rightarrow0^{-}}f\left(x\right)=0$ , $\lim_{x\rightarrow0^{+}}f\left(x\right)=0$ , $\lim_{x\rightarrow0}f\left(x\right)=0$

B

$\lim_{x\rightarrow0^{-}}f\left(x\right)=0$ , $\lim_{x\rightarrow0^{+}}f\left(x\right)=0$ , $\lim_{x\rightarrow0}f\left(x\right)=DNE$

C

$\lim_{x\rightarrow0^{-}}f\left(x\right)=-1$ , $\lim_{x\rightarrow0^{+}}f\left(x\right)=-1$ , $\lim_{x\rightarrow0}f\left(x\right)=DNE$ $\lim_{x\rightarrow0}f\left(x\right)=-1$

D

$\lim_{x\rightarrow0^{-}}f\left(x\right)=-1$ , $\lim_{x\rightarrow0^{+}}f\left(x\right)=-1$ , $\lim_{x\rightarrow0}f\left(x\right)=-1$

12

Problem

Problem

Using the graph, find the specified limit or state that the limit does not exist.
$\lim_{x\rightarrow4^{-}}f\left(x\right)$ , $\lim_{x\rightarrow4^{+}}f\left(x\right)$ , $\lim_{x\rightarrow4}f\left(x\right)$

A

$\lim_{x\rightarrow4^{-}}f\left(x\right)=1$ , $\lim_{x\rightarrow4^{+}}f\left(x\right)=1$ , $\lim_{x\rightarrow4}f\left(x\right)=1$

B

$\lim_{x\rightarrow4^{-}}f\left(x\right)=3$ , $\lim_{x\rightarrow4^{+}}f\left(x\right)=3$ , $\lim_{x\rightarrow4}f\left(x\right)=3$

C

$\lim_{x\rightarrow4^{-}}f\left(x\right)=3$ , $\lim_{x\rightarrow4^{+}}f\left(x\right)=1$ , $\lim_{x\rightarrow4}f\left(x\right)=DNE$

D

$\lim_{x\rightarrow4^{-}}f\left(x\right)=1$ , $\lim_{x\rightarrow4^{+}}f\left(x\right)=3$ , $\lim_{x\rightarrow4}f\left(x\right)=DNE$

13

Problem

Problem

Find the specified limit or state that the limit does not exist by creating a table of values.
$f\left(x\right)=\frac{1}{x}$
$\lim_{x\rightarrow1^{-}}f\left(x\right)$ , $\lim_{x\rightarrow1^{+}}f\left(x\right)$ , $\lim_{x\rightarrow1}f\left(x\right)$

A

$\lim_{x\rightarrow1^{-}}f\left(x\right)=0$ , $\lim_{x\rightarrow1^{+}}f\left(x\right)=0$ , $\lim_{x\rightarrow1}f\left(x\right)=1$

B

$\lim_{x\rightarrow1^{-}}f\left(x\right)=1$ , $\lim_{x\rightarrow1^{+}}f\left(x\right)=1$ , $\lim_{x\rightarrow1}f\left(x\right)=1$ $\lim_{x\rightarrow x}f\left(x\right)=1$

C

$\lim_{x\rightarrow1^{-}}f\left(x\right)=1$ , $\lim_{x\rightarrow1^{+}}f\left(x\right)=-1$ , $\lim_{x\rightarrow1}f\left(x\right)=DNE$

D

$\lim_{x\rightarrow1^{-}}f\left(x\right)=-1$ , $\lim_{x\rightarrow1^{+}}f\left(x\right)=-1$ , $\lim_{x\rightarrow1}f\left(x\right)=-1$

14

concept

Cases Where Limits Do Not Exist

Video duration:

3m

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15

example

Cases Where Limits Do Not Exist Example 2

Video duration:

3m

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16

Problem

Problem

Use the graph of $f\left(x\right)$ to estimate the value of the limit or state that it does not exist (DNE).
$\lim_{x\rarr1}f\left(x\right)$

A

$0$

B

$1$

C

$2$

D

DNE

17

Problem

Problem

Use the graph of $f\left(x\right)$ to estimate the value of the limit or state that it does not exist (DNE).
$\lim_{x\rarr-2}f\left(x\right)$

A

$-3$

B

$1$

C

$4$

D

DNE

18

Problem

Problem

Use the graph of $f\left(x\right)$ to estimate the value of the limit or state that it does not exist (DNE).
$\lim_{x\rarr0}f\left(x\right)$

A

$0$

B

$1$

C

$5$

D

DNE

19

Problem

Problem

Use the graph of $f\left(x\right)$ to estimate the value of the limit or state that it does not exist (DNE).
$\lim_{x\rarr-2}f\left(x\right)$

A

$-1$

B

$0$

C

$1$

D

DNE

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