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Lim(n->oo)[1/n^2 * sec^2 (1/n^2)+2/n^2 *...

`Lim_(n->oo)[1/n^2 * sec^2 (1/n^2)+2/n^2 * sec^2 (4/n^2)+..............+1/n * sec^2 1]`

A

`1/2 sec 1`

B

`1/2 cosec 1`

C

`tan 1`

D

` 1/2 tan 1`

Text Solution

Verified by Experts

The correct Answer is:
D
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MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
  1. lim(n->oo)[(1+1/n^2)(1+2^2 /n^2)(1+3^2 /n^2)......(1+n^2 / n^2)]^(1/n)

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  2. underset(nrarroo)"lim"[sin'(pi)/(n)+sin'(2pi)/(n)+"......"+sin'((n-1))...

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  3. Lim(n->oo)[1/n^2 * sec^2 (1/n^2)+2/n^2 * sec^2 (4/n^2)+..............+...

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  4. If int (0)^(x^(2)) f(t) dt = x cos pix , then the value of f(4) is

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  5. If C0/1+C1/2+C2/3=0 , where C0 C1, C2 are all real, the equation C2x...

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  6. Let I (1) = int (1) ^(2) (dx )/(sqrt(1 + x ^(2))) and I (2) = int (1) ...

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  7. If I(n)=underset(0)overset(pi//4)inttan^(n)x dx, then (1)/(I(2)+I(4)...

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  8. If I (1) = int (0) ^(1) 2 ^(x ^(2)) dx, I (2) = int (0) ^(1) 2 ^(x ^(3...

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  9. If u (n) = int (0) ^(pi//2) x ^(n) sin x dx, n in N then the value of ...

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  10. The vlaue of the integral underset(-1)overset(3 )int ("tan"^(1)(x)/(...

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  11. In = int0^(pi/4) tan^n x dx , then the value of n(l(n-1) + I(n+1)) is

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  12. The value of the integral l = int(0)^(1) x(1-x)^(n) dx is

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  13. Let I (1) = int (0) ^(1) (e ^(x) dx )/( 1 + x) and I (2) = int (0) ^(1...

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  14. If f(x) is a function satisfying f(1/x)+x^2f(x)=0 for all nonzero x , ...

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  15. If underset(0)overset(100)intf(x) dx = a, then underset(r=1)overset(10...

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  19. Find the value of the function f(x)=1+x+int1^x((lnt)^2+2lnt) dt where ...

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  20. If f(x)=e^(g(x))a n dg(x)=int2^x(tdt)/(1+t^4) then f^(prime)(2) has th...

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