Question

code class="asciimath">\lim_(x->\infty )\sqrt(x)*sin((1)/(x)) $\lim_{x \to 0} \sqrt{x} \cdot \sin \frac{1}{x}$

Name: code classasciimathlimx infty sqrtxsin1x limx to 0 sqrtx cdot sin frac1x 47756
Uploaded: 2021-07-31T21:19:24-08:00
Duration: 1 min 26 s
Channel: Nick Johnson
Description: code classasciimathlimx infty sqrtxsin1x limx to 0 sqrtx cdot sin frac1x 47756

          code class="asciimath">\lim_(x->\infty )\sqrt(x)*sin((1)/(x))
$\lim_{x \to 0} \sqrt{x} \cdot \sin \frac{1}{x}$

$code classasciimathlimx infty sqrtxsin1x limx to 0 sqrtx cdot sin frac1x 47756$

Added by Brandi W.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Nick Johnson

07/31/2021

Step 1

We have $$ L = \lim_{x \to 0} \sqrt{x} \cdot \sin \frac{1}{x} $$ Since $-1 \le \sin \frac{1}{x} \le 1$ for all $x \ne 0$, we have $$ -\sqrt{x} \le \sqrt{x} \sin \frac{1}{x} \le \sqrt{x} $$ Show more…

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