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

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Answer 1 · 2018-06-05T18:52:26

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

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

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