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underset(xtooo)lim(x^(2)"tan"(1)/(x))/(s...

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

A

`(pi)/2`

B

`(pi)/4`

C

1

D

`pi`

Text Solution

Verified by Experts

The correct Answer is:
A
`lim_(xto oo) (int_(0)^(x)tan^(-1)tdt)/(sqrt(x^(2)+1))` (`(oo)/(oo)` form)
`=lim_(xto oo) (tan^(-1))/(x/(sqrt(x^(2)+1)))`
`=(pi)/2 lim_(xto oo) (sqrt(x^(2)+1))/x`
`=(pi)/2 lim_(xto oo) sqrt(1+1/(x^(2)))=(pi)/2`
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CENGAGE-DEFINITE INTEGRATION -Exercise (Single)
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  2. The value of int(1/e)^(tanx)(tdt)/(1+t^2)+int(1/e)^(cotx)(dt)/(t(1+t^2...

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

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  4. A function f is defined by f(x) = int0^pi cos t cos(x-t)dt,0 <= x <= 2...

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  5. If f' is a differentiable function satisfying f(x)=int(0)^(x)sqrt(1-f^...

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  6. Ifint0^1e^x^2(x-alpha)dx=0,t h e n a<alpha<2 (b) alpha<0 0<alpha<1 ...

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  7. The function x^x decreases in the interval (0,e) (b) (0,1) (0,1/e) ...

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  8. Given that f satisfies |f(u)-f(v)|lt=|u-v|forua n dv in [a , b]dot The...

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  9. ("lim")(xvecoo)(x(log"x")^3)/(1+x+x^2)e q u a l 0 (b) -1 (c) 1 ...

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  10. int0^oo(pi/(1+pi^2x^2)-1/(1+x^2))logxdxi se q u a lto -pi/21npi (b) ...

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  11. IfA=int0^pi(cosx)/((x+2)^2)dx ,t h e nint0^(pi/2)(sin2x)/(x+1)dxi se q...

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  12. int0^4((y^2-4y+5)sin(y-2)dy)/([2y^2-9y+11])i se q u a lto 0 (b) 2 ...

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  13. IF tan ( pi cos theta) = cot ( pi sin theta ) then cos ( theta ...

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  14. L e tI1=thetaint0^1(e^xdx)/(1+x)a n dI2thetaint0^1(x^2dx)/(e^x^3(2-x^3...

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  15. L e tI1=int(-2)^2(x^6+3x^5+7x^4)/(x^4+2)dxa n d I2=int(-3)^1(2(x+1)^2...

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  16. Let f beintegrable over [0,a] for any real value of a. If I(1)=int(0...

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  17. The value of inta^b(x-a)^3(b-x)^4dxi s ((b-a)^4)/(6^4) (b) ((b-a)^8)...

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  18. IfI(m , n)=int0^1x^(m-1)(1-x)^(n-1)dx ,(m , n in I ,m ,ngeq0),t h e n...

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  19. The value of the definite integral int0^(pi/2)(sin5x)/(sinx)dxi s 0 (...

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  20. IfIn=int0^pie^x(sin"x")^("n")dx ,t h e n(I3)/(I1)i se q u a lto 3/5 ...

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