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Evaluate: ("lim")(xvec0)x^x...

Evaluate: `("lim")_(xvec0)x^x`

A

`1//2`

B

2

C

1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
`1" and "0`
Let`y=x^(x)`
`:.logy=xlogx`
`:.underset(yto0)limlogy=underset(xto0)limxlogx`
`=underset(xto0)lim(logx)/(1//x)" "((oo)/(oo)" form")`
`=underset(xto0)lim(1//x)/(-1//x^(2))`
`=underset(xto0)lim(logx)/(1//x)" "((oo)/(oo)" form")`
`=underset(xto0)lim(1//x)/(-1//x^(2))`
`:." "y=1`
`=underset(xto0^(+))limx^(x^(x))=(0^(+))^(1)=0`
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