in Calculus edited by
1,915 views
0 votes
0 votes
$lim_{x ->0}$ (x log sin x) is

a) 0

b) 1/2

c) 1

d) 2
in Calculus edited by
by
1.9k views

1 Answer

3 votes
3 votes

For small values of x, sin(x) is approximately equal to x. Since the limit is approaching to a smaller value, we can assume this. The approximation "x  sin(x) for small values of x" is a useful estimation tool.

Now, limx->0 x log(sin x) = limx->0 x log(x) = limx->0  (log(x) / (1/x)). Now as x approaches to 0, log(x) approaches to infinity and (1/x) too approaches to infinity (easily seen if we plot the graph). Therefore we can apply l'Hospital rule as it's a (∞/∞) form. 

Differentiating numerator and denominator, we get finally (-x / ln 10). Putting limit to it, we get 0 as the answer. 

Option (a)

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