Limit questions
411 published questions with worked solutions.
- The value of _ x 0 ( x^2 ^2x x^2- ^2x ) is:
- _ x 2 ( _ x^3 ^ ( /2)^3 ( (2t^ 1/3 ) + (t^ 1/3 ))dt (x - 2 )^2 ) is equal to :
- If _ x 0 3 + x + x + _e(1 - x) 3 ^2x = 13, then 2α – β is equal to:
- If a = _ x 0 1+ 1+x^4 - 2 x^4 and b = _ x 0 ^2x 2- 1+ x , then the value of ab³ is :
- Let the slope of the line 45x + 5y + 3 = 0 be 27r_1 + 9r_2 2 for some r₁, r₂ ∈ ℝ. Then _ x 3 ( _3^x 8t^2 3r_2x 2 - r_2x^2 -...
- _ x 2 ( 1 (x- 2 )^2 _ x^3 ^ ( 2 )^3 (t^ 1/3 )dt ) is equal to-
- Let f : [−π/2, π/2] → ℝ be a differentiable function such that f(0) = 1/2. If _ x 0 x _0^xf(t)dt e^ x^2 - 1 = , then 8α² is equal...
- Let f : ℝ → (0, ∞) be a strictly increasing function such that _ x f(7x) f(x) = 1. Then, the value of _ x [ f(5x) f(x) - 1 ] is...
- If _ x 0 ax^2e^x - b _e(1+x) + cxe^ -x x^2 x = 1, then 16(a² + b² + c²) is equal to ________.
- _ x 0 e^ 2| x| - 2| x| - 1 x^2
- Let f : R R be a continuous function. Then _ x 4 _ /4 ^ ^2x f(x)dx x^2- ^2 16 is equal to :
- If _ x 0 ae^x-b x+ce^ -x x x =2, then a + b + c is equal to _______.
- The value of the limit _ 0 ( ^2 ) (2 ^2 ) is equal to :
- The value of _ x 0^+ ^ -1 (x-[x]^2) ^ -1 (x-[x]^2) x-x^3 [x] denotes the greatest integer x is :
- If _ x 0 ^ -1 x- ^ -1 x 3x^3 is equal to L, then the value of (6L + 1) is equal to :
- If _ x 0 xe^x- _e(1+x)+ x^2e^ -x x ^2x =10, , , R then the value of + + is _____.
- If the value of _ x 0 (2- x 2x )^ ( x+2 x^2 ) is equal to e^a, then a is equal to _____.
- _ x 0^+ _0^ x^2 ( t)dt x^3 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
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