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Evaluate lim(x-> 0) (tan3x-2x)/(3x- sin^...

Evaluate `lim_(x-> 0) (tan3x-2x)/(3x- sin^2 x)`

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`lim_(x-> 0) (tan3x-2x)/(3x- sin^2 x)`

We know,

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

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

`lim_(x-> 0) (tan3x-2x)/(3x- sin^2 x)=lim_(x-> 0) (3x*1-2x)/(3x- x^2)`

`lim_(x-> 0) (x)/(3x- x^2)`

`lim_(x-> 0) (1)/(3- x)`

`=1/(3-0)=1/3`
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