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If f (x) = lim ( n to oo) (n (x ^(1//n)-...

If `f (x) = lim _( n to oo) (n (x ^(1//n)-1))` for ` x gt 0,` then which of the following is/are true?

A

`f ((1)/(x))=0`

B

` f ((1)/(x)) =(1)/(f (x))`

C

`f ((1)/(x)) =-f (x)`

D

`f (xy)=f (x)+ f(y)`

Text Solution

Verified by Experts

The correct Answer is:
C, D
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VIKAS GUPTA (BLACK BOOK)-LIMIT-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
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  7. If f (x) = lim ( n to oo) (n (x ^(1//n)-1)) for x gt 0, then which of...

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  13. Let f (x)= [{:(x+3,, -2 lt x lt 0),(4, x=0),(2x+5,, 0 lt x lt 1):}, t...

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  15. A certain function f (x) has the property that f (3x)=alpha f (x) for ...

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  17. Consider the limit lim (x to 0) (1)/(x ^(3))((1)/(sqrt(1+x))- ((1+ ax)...

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  18. Consider the limit lim (x to 0) (1)/(x ^(3))((1)/(sqrt(1+x))- ((1+ ax)...

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  19. For the curve sinx+siny=1 lying in first quadrant. If underset(xrarr0...

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