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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)
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  2. If("lim")(xvecoo)(n .3^n)/(n(x-2)^n+n .3^(n+1)-3^n)=1/3, t h e nt h e ...

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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")(xvecoo)1/((3/pitan^(-1)2x)^(2n)+5)dot 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")(xvecoo)[(2n)/(2n^2)cos(n+1)/(2n-1)-n/(1-2n)dot(n(...

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  7. If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f(pi/2)...

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  8. ("lim")(xvec1)(xsin(x-[x]))/(x-1),w h e r e[dot] denotes the greatest ...

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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")(xvec0)(x^asin^b x)/(sin(x^c)), where a , b , c in R ~{0},exis...

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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")(xvec1)(1-x^2)/(s in2pix)i se q u a lto 1/(2pi) (b) -1/pi (c...

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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")(xvec0)((x+y)sec(x+y)-xsecx)/yi se q u a lto (a)secx(xtanx+1)...

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  15. lim(xto0)(1+x)^(1/(3x))

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  16. ("lim")(n->oo)sum(x=1)^(20)cos^(2n)(x-10) is equal to (a) 0 (b) 1 (...

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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")(xvecoo)"{"x+5")"tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)} is equal to ...

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  19. The value of ("lim")(xvec0)([(100 x)/(sinx)]+[(99sinx)/x]) (where [.] ...

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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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