# Lim x—> 0 (1-cos4x)/(1-cos5x) Answer The Value ?

##### 1 Answer

Jun 5, 2018

#### Explanation:

We want to solve

#L=lim_(x->0)(1-cos(4x))/(1-cos(5x))#

Which is an indeterminate form

So we can apply **L'Hôpital's rule**

#color(blue)(lim_(x->c)f(x)/g(x)=lim_(x->c)(f'(x))/(g'(x))#

Thus

#L=lim_(x->0)(4sin(4x))/(5sin(5x))#

Again an indeterminate form

#L=lim_(x->0)(4*4*cos(4x))/(5*5*cos(5x))=16/25#