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underset(xrarroo)(lim)(cot^(-1)(sqrt(x+1...

`underset(xrarroo)(lim)(cot^(-1)(sqrt(x+1)+sqrtx))/(sec^(-1){((2x+1)/(x-1))^(x)})=`

A

1

B

0

C

`(pi)/(2)`

D

non-existent

Text Solution

Verified by Experts

The correct Answer is:
A
`lim_(xto oo) cot^-1(sqrt(x+1)-sqrt(x))/(sec^-1{((2x+1)/(x-1))^x})`
`lim_(xto oo) cot^-1((1)/(sqrt(x+1)-xsqrt(x)))/(sec^-1{(2+(3)/(x-1))^x})=(cot^-1(0))/sec^-1(oo)=(pi//2)/(pi//2)=1`
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OBJECTIVE RD SHARMA ENGLISH-LIMITS-Section I - Solved Mcqs
  1. The value of lim(n->oo) (1^2 . n+2^2.(n-1)+......+n^2 . 1)/(1^3+2^3+....

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  2. lim(nrarr oo) ((nsqrt(a)+nsqrt(b))/(2))^n,a,b,gt 0 equals

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  3. underset(xrarroo)(lim)(cot^(-1)(sqrt(x+1)+sqrtx))/(sec^(-1){((2x+1)/(x...

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  4. lim(xrarr 1) (x^(2^(32))-2^32x+4^16-1)/((x-1)^2) is equal to

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  5. The value of lim(xrarr oo) (3sqrt(x^3+x^2)-3sqrt(x^3-x^2)), is

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  6. If lim(xrarr-1)(sin(x^3+bx^2+cx +d))/((sqrt(2+x)-1){loge(x+2)}^2) exis...

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  7. If lim(xrarr1)(ax^2+bx+c)/((x-1)^2)=2, then lim(xrarr1)((x-a)(x-b)(x-c...

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  8. The value of lim(xrarr0) (loge(1+x)-x)/(x{(1+x)^(1//x)-e}) equal to

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  9. The value of lim(xrarr0) (sin(sinx)-tan(sinx))/(sin^3(sinx)), is

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  10. The value of lim(xrarr oo) x{(1)/(e)-((x)/(x+1))^x} , is

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  11. The value of lim(xrarr1){(x^n-1)/(n(x-1))}^((1)/(x-1)), is

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  12. If the equation of the normal to the curve y=f(x) at x=0 is 3x-y+3=0 t...

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  13. If lim(xrarr1)((asin(x-1)+bcos(x-1)+4))/(x^2-1)=2, then (a,b) is equal...

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  14. If a gt 0 and lim(xrarr oo) {sqrt(x^2+x+1)-(ax+b)}=0, then (a,b) lies ...

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  15. If alpha,beta are two distinct real roots of the equation a x ^3 + x-...

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  16. Let f(x)=(loge(x^2+e^x))/(loge(x^4+e^2x)). If lim(xrarr oo) f(x)=l and...

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  17. lim(nto oo) ((nsqrt(p)+nsqrt(q))/(2))^n,p,q,gt 0 equals

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  18. The value of lim(xrarr0)(e^(x)-cos2x-x)/(x^2) , is

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  19. lim(xrarr0) (2^(|x|)e^(|x|)-|x|log(2)2-1)/(xtanx) is equal to

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

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