Question

The limit $\lim_{x \to +\infty} \frac{1 - \sin(5x)}{1 - \sqrt{1 - \frac{3}{x}}}$ (A) equals -5/3 (B) equals $-\infty$ (C) equals 0 (D) equals -1/3 (E) does not exist

Name: the limit limx to infty frac1 sin5x1 sqrt1 frac3x a equals 53 b equals infty c equals 0 d equals 13 e does not exist 54752
Uploaded: 2021-10-03T17:06:59-08:00
Duration: 3 min 25 s
Channel: Abhijith V
Description: the limit limx to infty frac1 sin5x1 sqrt1 frac3x a equals 53 b equals infty c equals 0 d equals 13 e does not exist 54752

          The limit $\lim_{x \to +\infty} \frac{1 - \sin(5x)}{1 - \sqrt{1 - \frac{3}{x}}}$
(A) equals -5/3
(B) equals $-\infty$
(C) equals 0
(D) equals -1/3
(E) does not exist

$the limit limx to infty frac1 sin5x1 sqrt1 frac3x a equals 53 b equals infty c equals 0 d equals 13 e does not exist 54752$

Added by Matthew W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Abhijith V

10/03/2021

Step 1

We have $$ L = \lim_{x \to +\infty} \frac{1 - \sin(5x)}{1 - \sqrt{1 - \frac{3}{x}}} $$ Since $-1 \le \sin(5x) \le 1$, the numerator $1 - \sin(5x)$ is bounded between 0 and 2. Show more…

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The limit $\lim_{x \to +\infty} \frac{1 - \sin(5x)}{1 - \sqrt{1 - \frac{3}{x}}}$ (A) equals -5/3 (B) equals $-\infty$ (C) equals 0 (D) equals -1/3 (E) does not exist