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Problem

Find the limits. $$ \lim _{x \rightarrow+\infty}\…

02:13

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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72

Problem 36 Medium Difficulty

Find the limits.
$$
\lim _{x \rightarrow 0}\left(\frac{1}{x}-\frac{1}{e^{x}-1}\right)
$$

Answer

$$\lim _{x \rightarrow 0}\left(\frac{1}{x}-\frac{1}{e^{x}-1}\right)=\frac{1}{2}$$

Related Courses

Calculus 1 / AB

Calculus Early Transcendentals

Chapter 3

TOPICS IN DIFFERENTIATION

Section 6

L Hopital's Rule; Indeterminate Forms

Related Topics

Functions

Limits

Derivatives

Differentiation

Continuous Functions

Applications of the Derivative

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Video Transcript

We're starting with a limit as X goes to zero of one over X minus one over. Eat the X minus one. Um, so let's just go ahead and before doing anything else we write, this is a fraction. Okay, so here we just found common denominators in written in this a fraction. So now if we try to evaluate this limit, we see that we get zero on the top and we get zero on the bottom. So let's go ahead and use low Patel's rule reading LH for Low Patel's rule over the equals sign. And here in the numerator, where you take the derivative and we're going to get E to the X minus one, the dominator, we're going to have to do product room. So we have the derivative of X is one leaving us with E to the X minus one, and then we have X times e to the X, Okay. And trying to evaluate this woman, we see that we have 0/0. So we're actually going to have to do the Patel's role again. So the drone of the top is e to the X on the derivative bottom is e to the X plus e to the X plus X key to the X. And here this is a limit that we can evaluate. So on the top we get one Thebes nominator. We get one plus one plus zero LTD's one half.

We have video lessons for 84.11% of the questions in this textbook

Howard Anton, Irl Bivens, Stephen Davis

Calculus Early Transcendentals

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Related Topics

Functions

Limits

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