Limit questions
411 published questions with worked solutions.
- Let p = _ x 0^+ (1 + ^2 x )^ 1 2x then log p is equal to
- _ n ( (n + 1)(n + 2) 3n n^ 2n )^ 1 n is equal to -
- _ x 2 x - x ( - 2x)^3 equals :
- For each t R , let [t] be the greatest integer less than or equal to t. Then _ x 0^+ x ( [ 1 x ] + [ 2 x ] + + [ 15 x ] )
- _ x 0 (27 + x)^ 1/3 - 3 9 - (27 + x)^ 2/3 equals -
- _ x 0 ^2x 2 - 1+ x equals:
- Let f: R R be a differentiable function satisfying f'(3) + f'(2) = 0. Then _ x 0 ( 1 + f(3+x) - f(3) 1 + f(2-x) - f(2) )^ 1/x is...
- If _ x 1 x^2-ax+b x-1 = 5, then a + b is equal to:
- _ x 0 x 2x - 2x x (1 - 2x)^2 equals -
- If _ x 1 x^4 - 1 x - 1 = _ x k x^3 - k^3 x^2 - k^2 , then k is:
- For each x ∈ R, let [x] be the greatest integer less than or equal to x. Then _ x 0^- x([x] + |x|) [x] |x| is equal to:
- _ y 0 1 + 1 + y^4 - 2 y^4
- Let f: R → R be a continuously differentiable function such that f(2) = 6 and f'(2) = 1 48 . If _6^ f(x) 4t^3dt = (x - 2)g(x),...
- _ x 1^- - 2 ^ -1 x 1 - x is equal to:
- _ x /4 ^3x - x (x + 4 ) is:
- _ x 0 x (4x) ^2x ^2(2x) is equal to:
- Let [x] denote the greatest integer less than or equal to x. Then _ x 0 ( ^2x) + (|x| - (x[x]))^2 x^2
- For each t ∈ R, let [t] be the greatest integer less than or equal to t. Then _ x 1^+ (1 - |x| + |1 - x|) ( 2[1 - x] ) |1 - x|...
- _ x 0 x + 2 x x^2 + 2 x + 1 - ^2x - x + 1 is:
- Let f(x) = 5 − |x − 2| and g(x) = |x + 1|, x ∈ R. If f(x) attains maximum value at α and g(x) attains minimum value at β, then _...
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