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lim ( x to 0) ( e ^(x ^(2)) -c os x )/( ...

`lim _( x to 0) ( e ^(x ^(2)) -c os x )/( x ^(2)) = `

A

`3/2`

B

`1/2`

C

1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`lim_(xrarr0)(e^(x^2)-cosx)/(x^2)=lim_(xrarr0)(e^(x^2)-1+1-cosx)/(x^2)`
`=lim_(xrarr0)(e^(x^2)-1)/(x^2)+lim_(xrarr0)(2sin^(2)""(x)/(2))/(x^2)=1+1/2lim_(xrarr0)((sin""(x)/2)/(x/2))^(2)=1+1/2=3/2`
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