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Evaluate the following limit: (lim)(x->0...

Evaluate the following limit: `(lim)_(x->0)(cos3x-cos7x)/(x^2)`

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`(lim)_(x->0)(cos3x-cos7x)/(x^2)`

L'Hopital Rule:

`lim_(x rightarrow b) (f(x))/(g(x))=lim_(x rightarrow b) (f'(x))/(g'(x))`

`(lim)_(x->0)(-3sin3x+7sin7x)/(2x)`

We know,

`(lim)_(x->0) (sin x)/(x)=1`

`(lim)_(x->0)(-3*3x+7*7x)/(2x)`

`(lim)_(x->0)(-9+49)/(2)=20`

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