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Evaluate lim(xto0) (e^(x^(2))-cosx)/(x^(...

Evaluate `lim_(xto0) (e^(x^(2))-cosx)/(x^(2))`

Text Solution

Verified by Experts

The correct Answer is:
`3//2`
`underset(xto0)lim(e^(x^(2))-cosx)/(x^(2))=underset(xto0)lim[(e^(x^(2))-1)/(x^(2))+(1-cosx)/(x^(2))]`
`=1+underset(xto0)lim(2"sin"^(2)(x)/(2))/(x^(2))=1+(1)/(2)=(3)/(2)`
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