Limit questions
411 published questions with worked solutions.
- Let f:R R be a function such that f(2) = 4 and f'(2) = 1. Then, the value of _ x 2 x^2f(2)-4f(x) x-2 is equal to :
- The value of _ x 0 ( x [8] 1- x - [8] 1+ x ) is equal to :
- If U_n= (1+ 1 n^2 ) (1+ 2^2 n^2 )^2 (1+ n^2 n^2 )^n, then _ n (U_n)^ -4/n^2 is equal to :
- If , are the distinct roots of x^2+bx+c=0, then _ x e^ 2(x^2+bx+c) -1-2(x^2+bx+c) (x- )^2 is equal to :
- If _ x ( x^2-x+1 -ax)=b, then the ordered pair (a, b) is
- _ x 0 ^2( ^4x) x^4 is equal to :
- If _ x 0 ax-(e^ 4x -1) ax(e^ 4x -1) exists and is equal to b, then the value of a – 2b is _______.
- _ n (1+ 1+ 1 2 + + 1 n n^2 ) is equal to :
- The lowest integer which is greater than (1+ 1 10^ 100 )^ 10^ 100 is ——
- _ x 2 ( _ n=1 ^9 x n(n+1)x^2+2(2n+1)x+4 ) is equal to:
- _ x /4 (8 2 - ( x + sin x)^ 7 )/( 2 - 2 sin 2x) is equal to
- If _ n ( n^ 2 - n - 1 + n + ) = 0 then 8( + ) is equal to :
- _ x 2 ^2x ((2 ^2x + 3 x + 4)^ 1/2 - ( ^2x + 6 x + 2)^ 1/2 ) is equal to-
- Let f(x) be a polynomial function such that f(x) + f'(x) + f″(x) = x^ 5 + 64. Then, the value of _ x 1 f(x) x-1 is equal to :
- Let = _ x 0 ( x − (e^ 3x − 1))/( x(e^ 3x - 1)) for some R. Then the value of + is
- _ x 0 ( x) - x x^4 is equal to -
- _ x 1 2 ( ^ -1 x) - x 1 - ( ^ -1 x) is equal to :
- If = _ x /4 ^3x- x (x+ 4 ) and = _ x 0 ( x)^ x are the roots of the equation ax^2+bx-4=0, then the ordered pair (a, b) is :
- Let f(x) = x (1+x^n)^ 1/n , x R- -1 , n N, n > 2. if f^n(x) = (fofo……. upto n times) (x), then _ n _0^1x^ n-2 (f^n(x))dx is equal...
- The value of _ x 0 1 x^3 _0^x t , n(1+t) t^4+4 ,dt is
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