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The value of lim(x rarr 0) ((tanx^((1)/(...

The value of `lim_(x rarr 0) ((tanx^((1)/(5)))/((tan^(-1)sqrtx)^(2))(log(1+5x))/(e^(3root5x)-1))` is

A

`(3)/(5)`

B

`(5)/(3)`

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`L=underset(xrarr0^(+))(lim)(tanx^((1)/(5)))/(tan^(-1)sqrtx)(log(1+5x))/((e^(3root5x)-1))`
`=underset(xrarr0^(+))(lim)(tan(x^((1)/(5))))/(x^((1)/(5))).x^((1)/(5))((sqrtx)/(tan^(-1)sqrtx))^(2).(1)/(x).5x.((log(1+5x))/(5x))/(((e^(3.x^((1)/(5)))-1)/(3x^((1)/(5)))).3x^((1)/(5)))`
`=1.1.(loge)/(1).(5)/(3)=(5)/(3)`
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