Can anyone help me to find? the lim_(x rarr 0) (xcos2x)/(cos5x )

1 Answer
Oct 20, 2017

The answer is 0.

Explanation:

First, we should know that when lim_(x->0) f(x)and f(x) is a fraction, the constrain is that the denominator cannot be 0.

In this case, lim_(x->0) (xcos2x)/(cos5x) , if we just sub x=0 into the denominator, it will become cos(5*0)=cos0=1, which is not equal to 0.

So, we can just simply sub x=0 in this case and get the following:

lim_(x->0) (xcos2x)/(cos5x)=(0)(cos2(0))/(cos5(0)] =(0)(1)/(1)=0