If f(x)=lim(n->oo)n(x^(1/n)-1),t h e nfo...

If `f(x)=lim_(n->oo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y)` is equal to : (a)`f(x)f(y)` (b) `f(x)+f(y)` (c)`f(x)-f(y)` (d) none of these

`f(2x)+f(2y)`

`f(x)+f(y)`

`f(x+y)

`f(x)-f(y)`

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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