Question

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

Answer 1

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`