If f(x)=lim(ntooo) n(x^(1//n)-1)," then ...

If `f(x)=lim_(ntooo) n(x^(1//n)-1)," then for "xgt0, ygt0,f(xy)` is equal to

f(x)f(y)

f(x) + f(y)

f(x) - f(y)

none of these

Text Solution

Verified by Experts

The correct Answer is:

`f(x)=underset(ntooo)limn(x^(1//n)-1)`
`=underset(ntooo)lim(x^(1//n)-1)/(1//n)`
`=underset(mtooo)lim(x^(m)-1)/(m)" "("where "(1)/(n)" is replaced by m")`
`"ln "x`
or `f(xy)="ln "(xy)="ln "x+"ln "y=f(x)+f(y)`

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