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lim(x->0)(e^(x^(2))-cos x )/sin^2 xis eq...

`lim_(x->0)(e^(x^(2))-cos x )/sin^2 x`is equal to

A

3

B

`3//2`

C

`5//4`

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(x to 0)(lim)(e^(x^2)-cosx)/(sin^2 x)= underset(x to 0)(lim)(2xe^(x^2)+sinx)/(2sinx cosx)`
(using L' Hospital Rule)
`underset(x to 0)(lim)((x)/(sinx)e^(x^2)+1/2)1/(cosx)=1+1/2=3/2`
OR
`underset(x to 0)(lim)((e^(x^2)-1)+(1-cos x))/(x^(2)((sinx)/(x))^(2))`
`= (1+1//2)/((1)^(2)) = 3//2`
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