Limit questions
411 published questions with worked solutions.
- _ x a (a+2x)^ 1/3 -(3x)^ 1/3 (3a+x)^ 1/3 -(4x)^ 1/3 (a 0) is equal to -
- Let f(x) = _0^x(t + (1 - e^t))dt, x ∈ R. Then _ x 0 f(x) x^3 is equal to
- Let a > 0 be a root of the equation 2x² + x − 2 = 0. If _ x 1a 16 (1 - (2 + x - 2x^2) ) (1 - ax)^2 = + 17 , where α, β ∈ Z then α...
- Let f : (−∞, ∞) − 0 → R be a differentiable function such that f'(1) = _ a a^2f ( 1a ). Then _ a [ a(a + 1) 2 ^ -1 ( 1a ) + a^2 -...
- _ x 2 3^x+3^ 3-x -12 3^ -x/2 -3^ 1-x is equal to
- _ x 0 ( 3x^2+2 7x^2+2 )^ 1/x^2 is equal to -
- _ x 0 ( ( 4 +x ) )^ 1/x is equal to :
- _ n (1^2 - 1)(n - 1) + (2^2 - 2)(n - 2) + + ((n - 1)^2 - (n - 1)) 1 (1^3 + 2^3 + + n^3) - (1^2 + 2^2 + + n^2) is equal to
- If _ x 1 x+x^2+x^3+ +x^n-n x-1 =820, (n ∈ N) then the value of n is equal to_________.
- Let [t] denote the greatest integer ≤ t. If for some R- 0,1 , _ x 0 | 1-x+|x| -x+[x] |=L, then L is equal to-
- If _ x 0 1 x^8 (1- x^2 2 - x^2 4 + x^2 2 x^2 4 ) =2^ -k , then the value of k is __________ .
- The value of _ x 0 2 ( 1 - x 2x [3] 3x [10] 10x x^2 ) is ________.
- If α = _ x 0^+ ( e^ x - e^ x x - x ) and β = _ x 0 (1 + x)^ 12 x are the roots of the quadratic equation ax² + bx − √e = 0, then...
- If is the positive root of the equation, p(x)=x^2-x-2=0, then _ x ^+ 1- (p(x)) x+ -4 is equal to
- _ x 0 x(e^ ( 1+x^2+x^4 -1)/x -1) 1+x^2+x^4 -1
- _ x 1 ( _0^ (x-1)^2 t (t^2)dt (x-1) (x-1) )
- If _ x 2 (x^3 - 5x^2 + ax + b) ( x - 1 - 1) _e(x - 1) = m, then a + b + m is equal to:
- Let f(x)= _ y 0 (1- (xy)) (xy) y^3 . Then the number of solutions of the equation f(x)=sinx, x∈ℝ is:
- The product of all possible values of α, for which _ x 0 ( 1- ( x) (( +1)x) (( +2)x) ^2(( +1)x) )=2, is:
- Let _ x 2 ( (x-2))(rx^2+(p-2)x-2p) (x-2)^2 =5 for some r,p∈ℝ. If the set of all possible values of q, such that the roots of the...
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