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If I(1)=lim(xto oo)(tan^(-1)pi x- tan^(-...

If `I_(1)=lim_(xto oo)(tan^(-1)pi x- tan^(-1)x)cosx `and `I_(2)=lim_(xto0)(tan^(-1)pi x-tan^(-1)x)cosx` then `(I_(1),I_(2))` is

A

`(0,0)`

B

`(0,1)`

C

`(1,0)`

D

None of the above

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The correct Answer is:
A
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ARIHANT MATHS-LIMITS-Exercise (Single Option Correct Type Questions)
  1. lim(xto0)(sin(picos^(2)(tan(sinx))))/(x^(2)) is equal to

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  2. lim(t to0)(1-(1+t)^(t))/(In (1+t)-t) is equal to

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  3. If I(1)=lim(xto oo)(tan^(-1)pi x- tan^(-1)x)cosx and I(2)=lim(xto0)(ta...

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

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  5. lim (xto0) (""^(3)sqrt(1+sin ^(2)x )- ""^(4) sqrt(1-2 tan x))/(sin x+ ...

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  6. If x(n+1)=sqrt((1+xn)/2) and |x0|lt1 n in W then lim(n->oo)sqrt(1-x0...

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  7. For n in N, let f(n) (x) = tan ""(x)/(2) (1+ sec x ) (1+ sec 2x) (1+ s...

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  8. Let f(x) be a real valued function defined for all xge1, satistying f(...

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  9. The quadratic equation whose roots are the minimum value of sin^(2)the...

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  10. If x1=sqrt(3) and x(n+1)=(xn)/(1+sqrt(1+x n^2)),AA n in N then lim(n...

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  11. lim(xtoa^(-))(sqrt(x-b)-sqrt(a-b))/((x^(2)-a^(2))),(agtb) is

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

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

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  14. The value of lim sum(k=1)^n (n-k)/n cos((4k)/n) equals to

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  15. lim(x->0)(1-sqrt(cos2x)*root(3)(cos3x).....root(n)(cosnx))/x^2 has ...

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  16. lim(zto oo)(int(1//2)^(2)[cot^(-1)x]dx)/(int(1//2)^(z)[1+1/x]dx), wher...

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

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  18. 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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  19. Let f:(1,2)vecR satisfies the inequality (cos(2x-4)-33)/2<f(x)<(x^2|4x...

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

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