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lim(hto0)(1)/(h)int(x)^(x+h)(dz)/(z+sqrt...

`lim_(hto0)(1)/(h)int_(x)^(x+h)(dz)/(z+sqrt(z^(2)+1))` is equal to -

A

0

B

`(1)/(x+sqrt(x^(2)+1))`

C

`(1)/(sqrt(x^(2)+1))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(hto0)(lim)(overset(x+h)underset(x)int(dz)/(z+sqrt(z^(2)+1)))/(h),(0)/(0)`
Use L'Hospital Rule
`underset(hto0)(lim)((1)/(x+h+sqrt((x+h)^(2))+1).(0+1)-0)/(1)`
= `(1)/(x+sqrt(x^(2)+1))`
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