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Problem

Find the limits. $$ \lim _{x \rightarrow 0^{+}} x…

04:33

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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 38 Medium Difficulty

Find the limits.
$$
\lim _{x \rightarrow+\infty}[\ln x-\ln (1+x)]
$$

Answer

0

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

here. We're starting with a limit as X goes to infinity, the natural log of X minus natural log of one plus X. And if we try to evaluate this limit right away noticed that we get infinity minus infinity. So we're gonna go ahead and rewrite this. Let's go ahead and use our log properties. Okay, so now we have just ah, natural log here, and we're going to go ahead and use our limit interchange property that says that we can interchange the natural log with the limit because the natural log is a continuous function. Okay. And now here were set up to use low petals. Role because we have on infinity over infinity, huh? Form. So let's go ahead and use lot. Hotels rule the derivative of the numerator. Pecs is one. And the derivative of the denominator is one. Okay, so we get natural. Look of one that's equal to zero. That's your answer.

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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Functions

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