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lim(ntooo) n^(2)(x^(1//n)-x^(1//(n+1))),...

`lim_(ntooo) n^(2)(x^(1//n)-x^(1//(n+1))),xgt0,` is equal to

A

`pi`

B

`2pi`

C

`pi//2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(ntooo)limn^(2)(x^(1//n)-x^((1)/(n+1)))=underset(ntooo)limn^(2).x^((1)/(n+1))(x^((1)/(n)-(1)/(n+1))-1)`
`=underset(ntooo)limx^((1)/(n+1))(x^((1)/(n(n+1)))-1)n^(2)`
`=underset(ntooo)limx^((1)/(n+1)).(x^((1)/(n(n+1)))-1)/((1)/(n(n+1))).(n^(2))/(n(n+1))`
`=1.log_(e)x.1=log_(e)x`
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CENGAGE-LIMITS-Exercise (Single)
  1. lim(xtooo) (2sqrt(x)+3root(3)(x)+4root(4)(x)+...+nroot(n)(x))/(sqrt((2...

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  2. If lim(ntooo) (n.3^(n))/(n(x-2)^(n)+n.3^(n+1)-3^(n))=1/3, then the ran...

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  3. lim(ntooo) n^(2)(x^(1//n)-x^(1//(n+1))),xgt0, is equal to

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  4. Let f(x)=lim(ntooo) (1)/(((3)/(pi)tan^(-1)2x)^(2n)+5). Then the set of...

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  5. f(x)=("ln"(x^(2)+e^(x)))/("ln"(x^(4)+e^(2x))). Then lim(x to oo) f(x) ...

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  6. The value of lim(ntooo) [(2n)/(2n^(2)-1)"cos"(n+1)/(2n+1)-(n)/(1-2n).(...

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  7. If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f((pi)/...

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  8. lim(xto1) (xsin(x-[x]))/(x-1), where [.] denotes the greatest integer ...

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  9. lim(xtooo) (x^(2)"tan"(1)/(x))/(sqrt(8x^(2)+7x+1)) is equal to

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  10. lim(xto0) (x^(a)sin^(b)x)/(sin(x^(c))), where a,b,c inR~{0}, exists an...

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  11. lim(xto0) (x^(4)(cot^(4)x-cot^(2)x+1))/((tan^(4)x-tan^(2)x+1)) is equa...

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  12. lim(xto1) (1-x^(2))/(sin2pix) is equal to

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  13. lim(xto0) (1)/(x)cos^(1)((1-x^(2))/(1+x^2)) is equal to

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  14. lim(yto0) ((x+y)sec(x+y)-xsecx)/(y) is equal to

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  15. lim(xto1) (1+sinpi((3x)/(1+x^(2))))/(1+cospix) is equal to

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  16. lim(ntooo) sum(x=1)^(20)cos^(2n)(x-10) is equal to

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  17. lim(xto-1) ((x^(4)+x^(2)+x+1)/(x^(2)-x+1))^((1-cos(x+1))/(x+1)^(2)) is...

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  18. lim(xtooo) {(x+5)tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)} is equal to

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  19. The value of lim(xto0) ([(100x)/(sinx)]+[(99sinx)/(x)]) (where [.] rep...

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  20. The value of lim(xtoa) sqrt(a^(2)-x^(2))"cot"(pi)/(2)sqrt((a-x)/(a+x))...

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