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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(2x)+f(2y)`

B

`f(x)+f(y)`

C

`f(x+y)

D

`f(x)-f(y)`

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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CENGAGE-LIMITS-Exercise (Single)
  1. lim(xto0) [(1-e^(x))(sinx)/(|x|)] is (where [.] represents the greates...

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  2. Evaluate lim(xto0) (x(e^(x)-1))/(1-cosx) is equal to

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  3. If f(x)=lim(ntooo) n(x^(1//n)-1)," then for "xgt0, ygt0,f(xy) is equal...

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  4. lim(x to 0) {(1+x)^((2)/(x))} (where {.} denotes the fractional part o...

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  5. The value of lim(xtooo) ((2^(x^(n)))e^((1)/(x))-(3^(x^(n)))e^((1)/(x))...

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  6. lim(x to 0) (sin(x^(2)))/("ln"(cos(2x^(2)-x))) is equal to

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  7. lim(xtooo) (e^(1//x^(2))-1)/(2tan^(-1)(x^(2))-pi) is equal to

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  8. lim(xto0) ((2^(m)+x)^(1//m)-(2^(n)+x)^(1//n))/(x) is equal to

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  9. The value of lim(ntooo) [(1)/(n)+(e^(1//n))/(n)+(e^(2//n))/(n)+...+(e^...

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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(xto0) (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. lim(xto0) (cos(tanx)-cosx)/(x^(4)) is equal to

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  15. If lim(xto0) (x^(-3)sin3x+ax^(-2)+b) exists and is equal to 0, then

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  16. If lim(xto0) (x^(n)sin^(n)x)/(x^(n)-sin^(n)x) is non-zero finite, then...

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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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