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The value of int0^1lim(n->oo)sum(k =0)^n...

The value of `int_0^1lim_(n->oo)sum_(k =0)^n(x^(k+2)2^k)/(k!)dx` is: (a) `e ^(2) -1` (b) `2` (c) `(e ^(2)-1)/(2)` (d) `(e ^(2) -1)/(4)`

A

`e ^(2) -1`

B

`2`

C

`(e ^(2)-1)/(2()`

D

`(e ^(2) -1)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
D
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VK JAISWAL ENGLISH-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
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  3. If int (0)^(oo) (x ^(3))/((a ^(2)+ x ^(2)))dx = (1)/(ka ^(6)), then fi...

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  7. The value of int (tan x )/(tan ^(2) x + tan x+1)dx =x -(2)/(sqrtA) tan...

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  13. int( x^3)/(x^2-3)dx

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  14. If a continuous function f on [0,a] satisfies f(x)f(a-x)=1,agt0, then ...

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  15. If {x} denotes the fractional part of x, then I = int (0) ^(100) (sqrt...

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  17. If M be the maximum value of 72 int (0) ^(y) sqrt(x ^(4) +(y-y^(2))^(2...

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  18. Find the number points where f (theta) = int (-1)^(1) (sin theta dx )/...

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  19. Find the vlaur of lim (n to oo) (1)/(sqrtn)(1+ (1)/(sqrt2) +(1)/(sqrt3...

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  20. The maximum value of int (-pi/2) ^((3pi)/2) sin x. f (x) dx, subject t...

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  21. Given a function g, continous everywhere such that g (1)=5 and int (0)...

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