Limit questions
411 published questions with worked solutions.
- If _ x 0 [1 + x (1 + b^2) ]^ 1 x = 2b ^2 , b > 0 and (- , ], then the value of θ is
- If _ x ( x^2 + x + 1 x + 1 - ax - b ) = 4, then
- Let α(a) and β(a) be the roots of the equation ( [3] 1 + a - 1 )x^2 + ( 1 + a - 1 )x + ( [6] 1 + a - 1 ) = 0 where a > -1. Then _...
- The largest value of the nonnegative integer a for which _ x 1 -ax + (x - 1) + a x + (x - 1) - 1 ^ 1-x 1- x = 1 4 is
- Let m and n be two positive integers greater than 1. If _ 0 ( e^ ( ^n) -e ^m )=- ( e 2 ) then the value of m n is
- Let , R be such that _ x 0 x^2 ( x) x- x =1. Then 6( + ) equals
- Let f: R (0, ) and g: R R be twice differentiable functions such that f'' and g'' are continuous functions on R . Suppose...
- Let f: R R be a differentiable function such that f(0)=0, f ( 2 )=3 and f'(0)=1. If g(x)= _x^ 2 [f'(t) cosec t- t cosec t ,f(t)]...
- Let f(x)= 1-x(1+|1-x|) |1-x| ( 1 1-x ) for x 1. Then
- Let f: R R be a function. We say that f has PROPERTY 1 if _ h 0 f(h)-f(0) |h| exists and is finite, and PROPERTY 2 if _ h 0...
- The limit of f(x) = x^2 as x tends to zero equals
- Consider the function f(x) = cases 1, & x 0 2, & x > 0 cases Then, left hand limit and right hand limit of f(x) at x = 0, are...
- _ n 3 ( _ r=1 ^ n r^2 ) is equal to
- Value of _ y 2 [(y^3 - 3)(y + 2)] is
- Value of _ x 3 ( 6 + x - 7 - x x ) is
- The left hand limit of 1 x + 1 2 x + 2 at x = -2 is
- The limit of the function, f(x) = cases |x-3| x-3 , & x 3 0, & x = 3 cases at x = 3 is
- The value of _ x 3 (x^4 + x^3 - 3x) is
- The value of _ x 4 4x + 3 x - 2 is
- The value of _ x 1 (1+x)^6 - 1 (1+x)^2 - 1 is
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