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

Evaluate the following limit: `(lim)_(x->0)(xcosx+2\ sin x)/(x^2+tanx)`

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`(lim)_(x->0)(xcosx+2\ sin x)/(x^2+tanx)`

We know,

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

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

`(lim)_(x->0)(xcosx+2x)/(x^2+x)`

`(lim)_(x->0)(cosx+2)/(x+1)`

`=(cos0+2)/(0+1)`

`=(1+2)/(0+1)=3`
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