`lim_(x->0)[e^sinx-1]/x` – InterviewSolution

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1.	`lim_(x->0)[e^sinx-1]/x`
Answer» We know, `e^x = 1+x+x^2/2+x^3/3+...` `:. lim_(x->0) (e^(sinx)-1)/x = lim_(x->0) ((1+sinx+(sinx)^2/2+(sinx)^3/3+...) -1)/x` `= lim_(x->0) (sinx/x+sinx/xsinx+sinx/xsin^2x+...)` We know, `lim_(x->0) sinx/x = 1` and `lim_(x->0) sin x = 0` `:. lim_(x->0) (e^(sinx)-1)/x = 1+1(0)+1(0)+... = 1`

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