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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

A

f(x)f(y)

B

f(x) + f(y)

C

f(x) - f(y)

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`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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  10. lim(xto1) (nx^(n-1)-(n+1)x^(n)+1)/((e^(x)-e)sinpix), where n=100,is eq...

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  11. lim(xto0) (log(1+x+x^(2))+log(1-x+x^(2)))/(secx-cosx)=

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  12. The value of lim(xtooo) (root(3)(x^(3)+2x^(2))-sqrt(x^(2)+x)) is

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  13. The value of lim(xto0) (1+sinx-cosx+log(1-x))/(x^(3)) is

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  14. If lim(xtoa)f(x)=1 and lim(xtoa)g(x)=oo then lim(xtoa){f(x)}^(g(x))=e^...

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  15. If ("lim")(xvec0)(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, th...

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  16. If lim(x->0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must b...

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  17. lim(xto0) ((1+tanx)/(1+sinx))^(cosecx) is equal to

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  18. The value of lim(xto1) (2-x)^(tan((pix)/(2))) is

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  19. The value of lim(mtooo) ("cos"(x)/(m))^(m) is

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  20. lim(ntooo) ((n^(2)-n+1)/(n^(2)-n-1))^(n(n-1)) is equal to

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