Find the limit by creating a table of values. lim ⁡ x → 0 − 4 x + 2 \lim_{x\rarr0}-4x+2 lim x → 0 − 4 x + 2

In this problem, we're asked to find the limit by creating a table of values, and the limit that we wanna find here is the limit of negative 4x+2 as x approaches 0. Now here, since we're trying to find the limit as x approaches 0, we want to look at values really, really close to 0. So by creating a table of values here, I'm going to put 0 in the middle because I want to look at values getting really, really close to 0 on this side but are actually less than 0. So values like negative 0.01 and negative 0.1. Now I wanna plug these values into my function, negative 4 x plus 2. So doing that for this first value of negative 0.1, I get negative 4 times negative 0.1 plus 2 which will give me a value of 2.04. Now if I do the same thing here for this negative 0.01, this will actually give me a value of 2.004. So we can already see here that these values seem to be approaching 2 for my function as x approaches 0. But we, of course, want to look at values that are actually greater than 0 but really, really close to it, again, approaching 0 from this other side. So So I wanna think of values like a 0.01 and a 0.1. Now plugging these values into my function here, if I plug in this 0.01, that's going to give me a value of 1.96. And if I do the same thing for 0.1, again, plugging that into my function and negative 4x+2, that will give me a value of 1.6. So we see coming in from this side that we are again approaching 2 the same way that we saw on that left side. So here, the limit of negative 4x plus 2 as x approaches 0 is going to be equal to 2. And that's our limit here. I'll see you in the next one.

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0. Fundamental Concepts of Algebra3h 29m
1. Equations and Inequalities3h 27m
2. Graphs1h 43m
3. Functions & Graphs2h 17m
4. Polynomial Functions1h 54m
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6. Exponential and Logarithmic Functions2h 28m
7. Measuring Angles40m
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11. Inverse Trigonometric Functions and Basic Trig Equations1h 41m
12. Trigonometric Identities 2h 34m
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14. Vectors2h 25m
15. Polar Equations2h 5m
16. Parametric Equations1h 6m
17. Graphing Complex Numbers1h 7m
18. Systems of Equations and Matrices3h 6m
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20. Sequences, Series & Induction1h 15m
21. Combinatorics and Probability1h 45m
22. Limits & Continuity1h 49m
23. Intro to Derivatives & Area Under the Curve2h 9m

22. Limits & Continuity

Introduction to Limits

Precalculus

22. Limits & Continuity

Introduction to Limits

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Multiple Choice

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

$-4$

$-2$

$0$

$2$

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Verified step by step guidance

Understand the problem: We need to find the limit of the function as x approaches 0. The function given is -4x + 2.

Create a table of values: Choose values of x that are close to 0 from the left side (negative values) and calculate the corresponding values of the function -4x + 2.

Calculate the function values: For each chosen x value, substitute it into the function -4x + 2 and compute the result.

Observe the pattern: As x gets closer to 0 from the left, observe how the function values change. This will help you determine the limit.

Conclude the limit: Based on the pattern observed in the table, determine the limit of the function as x approaches 0 from the left.

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Find the limit by creating a table of values.lim⁡x→0−4x+2\lim_{x\rarr0}-4x+2limx→0​−4x+2

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