Question

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

Answer 1

`L=lim_(x->0)(1-cos(4x))/(1-cos(5x))=16/25`

Explanation:

We want to solve

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

Which is an indeterminate form `0/0`

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 `0/0`, so apply LHR again

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