The Gateway to Computer Science Excellence
0 votes
39 views

If $f(x) = \sin \bigg( \dfrac{1}{x^2+1} \bigg),$ then

  1. $f(x)$ is continuous at $x=0$, but not differentiable at $x=0$
  2. $f(x)$ is differentiable at $x=0$, and $f’(0) \neq 0$
  3. $f(x)$ is differentiable at $x=0$, and $f’(0) = 0$
  4. None of the above
in Calculus by Veteran (431k points)
recategorized by | 39 views

1 Answer

0 votes

Here, $\sin\left(\frac{1}{x^{2}+1}\right)$ is continuous and definitely differentiable.

$f(x)=\sin\left(\frac{1}{x^{2}+1}\right)\\ \Rightarrow f'(x)= \frac{-2x}{\left(x^{2}+1\right)^2}\cos\left(\frac{1}{x^{2}+1}\right)\\ \Rightarrow f'(0)=0$

 

So the correct answer is C.

 

by Active (3.5k points)
0

Here's the graph of $\sin\left(\frac{1}{x^{2}+1}\right)$ below.

 

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
50,737 questions
57,291 answers
198,209 comments
104,892 users