Continuity and Differentiability questions
732 published questions with worked solutions.
- If f(x) = cases 3 x 5x , & x 0 2k, & x = 0 cases is continuous at x = 0, then the value of k is equal to
- In order that the function f(x) = (x + 1)^ 1 x is continuous at x = 0, f(0) must be defined as
- If f(x) = cases 1 + kx - 1 - kx x , & for -1 x < 0 [1mm] 2x^2 + 3x - 2, & for 0 x 1 cases , is continuous at x = 0, then k =
- If f(x) = cases ax^2 - b, & when 0 x < 1 2, & when x = 1 x + 1, & when 1 < x 2 cases is continuous at x = 1, then the most...
- If f(x) = cases 1 - x - 2x , & x 2 [1mm] , & x = 2 cases be continuous at x = 2 , then value of is
- If f(x) = cases 1 - 2 x - 4x , & x 4 [1mm] a, & x = 4 cases is continuous at x = 4 , then a =
- The function f(x) = 2x^2 + 7 x^3 + 3x^2 - x - 3 is discontinuous for
- If f(x) = cases x^4 - 16 x - 2 , & when x 2 16, & when x = 2 cases , then
- If f(x) = cases x^2, & x 1 x + 5, & when x > 1 cases , then
- The function f(x) = |x| x^2 + 2x , x 0 and f(0) = 0 is not continuous at x = 0 because
- If f(x) = cases |x - a| x - a , & when x a 1, & when x = a cases , then
- The function f(x) = |x| + |x| x is
- If f(x) = cases x - |x| x , & when x 0 2, & when x = 0 cases , then
- The number of discontinuities of the greatest integer function f(x) = [x], x (- 7 2 , 100 ) is equal to
- If f(x) = cases x^2 - 4x + 3 x^2 - 1 , & for x 1 [1mm] 2, & for x = 1 cases , then
- The number of points at which the function f(x) = 1 |x| is discontinuous are
- If f(x) = cases x - 1, & x < 0 1 4 , & x = 0 x^2, & x > 0 cases , then
- For the function f(x) = cases e^ 1/x - 1 e^ 1/x + 1 , & x 0 0, & x = 0 cases , which of the following is correct
- The value of A and B such that the function f(x) = cases -2 x, & x - 2 A x + B, & - 2 < x < 2 x, & x 2 cases is continuous...
- If f is continuous at x = 0, where f(x) = (1 + x^2) - (1 - x^2) x - x for x 0, then f(0) =
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