Limit questions
411 published questions with worked solutions.
- Let g(x) = (x-1)^n ^m(x-1) ; 0 < x < 2, m and n are integers , m 0, n > 0, and let p be the left hand derivative of |x-1| at x =...
- _ x 0 (1- 2x)(3+ x) x 4x is equal to -
- Let f : R (0, ) be a twice differentiable function such that f(3) = 18, f'(3) = 0 and f''(3) = 4. Then _ x 1 ( _e ( f(2+x) f(3)...
- If _ x 0 e^ (a-1)x + 2 bx + (c-2)e^ -x x x - _e(1+x) = 2, then a^2+b^2+c^2 is equal to :
- The value of _ x 0 _e ( (ex) (e^2x) (e^ 10 x) ) e^2 - e^ 2 x is equal to
- If _ r=1 ^ n T_r = (2n-1)(2n+1)(2n+3)(2n+5) 64 , then _ n _ r=1 ^ n ( 1 T_r ) is equal to :
- If _ x ( ( e 1-e ) ( 1 e - x 1+x ) )^x = , then the value of _e 1+ _e equals :
- _ x (2x^2 - 3x + 5)(3x-1)^ x/2 (3x^2+5x+4) (3x+2)^x is equal to:
- Let f : R - 0 R be a function such that f(x) - 6f ( 1 x ) = 35 3x - 5 2 . If the _ x 0 ( 1 x + f(x) ) = ; , R, then + 2 is equal...
- Let f(x)= _ n _ r=0 ^n ( (x/2^ r+1 )+ ^3(x/2^ r+1 ) 1- ^2(x/2^ r+1 ) ). Then _ x 0 e^x-e^ f(x) (x-f(x)) is equal to ____.
- The value of _ n ( _ k=1 ^ n k^3+6k^2+11k+5 (k+3)! ) is :
- If _ t 0 ( _0^1(3x+5)^t ,dx )^ 1/t = 5e ( 8 5 )^ 2/3 , then is equal to _____.
- If _ x 0 (2x) + a (4x) - b x^4 is finite, then (a + b) is equal to :
- For α, β, γ ∈ R , if _ x 0 x^2 x + ( -1)e^ x^2 2x - x = 3, then β + γ – α is equal to :
- If _ x 0 ( x x )^ 1 x^2 = p, then 96 _e p is equal to ______.
- If _ x 1 (x-1)(6+ (x-1))+ (1-x) (x-1)^3 = -1, where λ, μ ∈ ℝ, then λ + μ is equal to
- Given below are two statements. Statement I: _ x 0 ( ^ -1 x + _e 1+x 1-x - 2x x^5 ) = 2 5 Statement II : _ x 1 (x^ 2 1-x ) = 1...
- The equivalent definition of the function f(x)= _ n x^n-x^ -n x^n+x^ -n , x>0, is
- In a ABC, the angles A,B,C are in AP. Then _ A C 3-4 A C |A-C| is equal to
- _ x 0 ( ^2 x) x^2 is equal to
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