Home
Class 11
MATHS
lim(x->0)[e^sinx-1]/x...

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

Text Solution

Verified by Experts

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/x*sinx+sinx/x*sin^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`
Promotional Banner

Similar Questions

Explore conceptually related problems

lim_(xto0)(e^(sinx)-1)/x=

Evaluate: lim_(x->0)(e^(sinx)-(1+sinx))/({tan^(-1)(sinx)}^2)

lim_(x->0) (2e^sinx-e^(-sinx)-1)/(x^2+2x)

lim_(x->0) (e^[[|sinx|]])/([x+1]) is , where [.] denotes the greatest integer function.

The value of lim_(x->0)((sinx)^(1/x)+(1/x)^(sinx)) , where x >0, is (a)0 (b) -1 (c) 1 (d) 2

The value of lim_(x->0)((sinx)^(1/x)+(1/x)^(sinx)) , where x >0, is (a)0 (b) -1 (c) 1 (d) 2

The value of lim_(x->0)((sinx)^(1/x)+(1/x)^(sinx)) , where x >0, is (a)0 (b) -1 (c) 1 (d) 2

The value of lim_(x->0)((sinx)^(1/x)+(1/x)^(sinx)) , where x >0, is 0 (b) -1 (c) 1 (d) 2

lim_(x to 0)(e^(sinx)-1)/x=.......

Evaluate the following limits : lim_(x to 0)(e^(sinx)-1)/x