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lim(xrarroo) {(e^(x)+pi^(x))^((1)/(x))}=...

`lim_(xrarroo) {(e^(x)+pi^(x))^((1)/(x))}`= (where {.} denotes the fractional part of x ) is equal to

A

`pi-e`

B

`pi-3`

C

`e-2`

D

`3-e`

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(xrarroo)(lim)(e^(x)+pi^(x))^(1//x)=piunderset(xrarroo)(lim)(((e)/(pi))^(x)+1)^(1//x)=pi`
Now, `{pi}=pi-3`
`therefore" "underset(xrarroo)(lim){(x^(x)+pi^(x))^(1)/(x))}=pi-3`
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