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The value of lim(xto0)2/(x^(3))(sin^(-1)...

The value of `lim_(xto0)2/(x^(3))(sin^(-1)x-tan^(-1)x)^(2//x^(3))` equals

A

`e`

B

`sqrt(e)`

C

`1/e`

D

`1/(sqrt(e))`

Text Solution

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The correct Answer is:
D
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ARIHANT MATHS-LIMITS-Exercise (Single Option Correct Type Questions)
  1. lim(xtoa^(-))(sqrt(x-b)-sqrt(a-b))/((x^(2)-a^(2))),(agtb) is

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  2. lim(ntooo)(sin^(n)1+cos^(n)1)^(n) is equal to

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  3. The value of lim(xto0)2/(x^(3))(sin^(-1)x-tan^(-1)x)^(2//x^(3)) equals

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  4. lim(nto oo)sum(r=1)^(n)r/(n^(2)+n+4) equals a. 0 b. 1/3 c. 1/2 d.1

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  5. Let U = {x : x ∈ N, x ≤ 9}; A = {x : x is an even number, 0 < x < 10};...

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  6. int(-1)^(2)[([x])/(1+x^(2))]dx, where [.] denotes the greatest integer...

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  7. If alpha and beta are roots of x^(2)-(sqrt(1-cos 2 theta))x+theta=0, w...

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  8. If f(x)=1/3(f(x+1)+5/(f(x+2))) and f(x)gt0,AA x epsilonR, then lim(xto...

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  9. Let f:(1,2)vecR satisfies the inequality (cos(2x-4)-33)/2ltf(x)lt(x^2|...

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  10. Let f(x) be polynomial of degree 4 with roots 1,2,3,4 and leading coef...

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  11. lim x→π/4 (4sqrt(2)-(cosx+sinx)^5)/(1−sin2x) is equal to

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  12. If lim(xto oo)(n.3^(n))/(n.(x-1)^(n)+n.3^(n+1)-3^(n))=1/3, the number ...

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

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  14. Find the integral value of n for which ("lim")(xvec0)(cos^2x-cosx-e^x...

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  15. Find dy/dx if x^7-e^x=siny

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  16. underset(xto(pi)/(2))(lim)([(x)/(2)])/(log(e)(sinx))([.] denotes great...

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  17. If tn=1/4(n+2)(n+3) for n=1,2,3, , then 1/(t1)+1/(t2)+1/(t3)++1/(t(20...

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  18. If f(x+ y) = f(x) + f(y) for x, y in R and f(1) = 1, then find the val...

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  19. Evaluate underset(ntooo)limn^(-n^(2))[(n+2^(0))(n+2^(-1))(n+2^(-2))......

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  20. If f(x)={("sin"[x])/([x]),for[x]!=0, 0,for[x]=0,where [x] denotes the...

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