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lim(xrarr0) (log(e^(x^(2))+2sqrtx))/(tan...

`lim_(xrarr0) (log(e^(x^(2))+2sqrtx))/(tansqrtx) ` is equal to

A

0

B

1

C

`e^(2)`

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(xrarr0)(lim)(log(e^(x^(2))+2sqrtx))/(tansqrtx)`
`" "=underset(xrarr0)(lim)(log(e^(x^(2))+2sqrtx))/((tansqrtx)/(sqrtx)sqrtx)`
`" "=underset(xrarr0)(lim)(log(e^(x^(2))+2sqrtx))/(sqrtx)`
`" "=underset(xrarr0)(lim)log(e^(x^(2))+2sqrtx)^((1)/(sqrtx))`
`" "=loge^(underset(xrarr0)(lim)(e^(x^(2))+2sqrtx-1)(1)/(sqrtx))`
`" "=loge^(underset(xrarr0)(lim)((e^(x^(2))-1)/(sqrtx)+2))`
`" "=2`
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CENGAGE PUBLICATION-LIMITS-Single Correct Answer Type
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  14. Let f : R rarr R be a differentiable function at x = 0 satisfying f(0)...

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