Continuity and Differentiability questions
732 published questions with worked solutions.
- Let f(x) = cases x 5x , & x 0 k, & x = 0 cases , if f(x) is continuous at x = 0, then k is equal to
- If f(x) = cases 1 - x x , & x 0 k, & x = 0 cases is continuous at x = 0, then the value of k is
- If f(x) = cases 1 + kx - 1 - kx x , & 1 x < 0 [1mm] 2x^2 + 3x - 2, & 0 x 1 cases is continuous at x = 0, then k is equal to
- If f(x) = cases x^k ( 1 x ), & x 0 0, & x = 0 cases is continuous at x = 0, then
- If f(x) = 1 + x - 1 - x x , then the value of f at x = 0, so that f is continuous everywhere, is
- The value of f(0), so that the function f(x) = 2x - ^ -1 x 2x + ^ -1 x is continuous at each point in its domain and is equal to
- If f(x) = cases x^2 1 x , & x 0 0, & x = 0 cases , then
- The set of points of continuity of the function f(x) = 1 2 - ^2 x is
- The function f(x) = [x], where [x] denotes the greatest integers x, is
- If the function f(x) = cases 1 - x x^2 , & x 0 k, & x = 0 cases is continuous at x = 0, then the value of k is
- If f(x) = 3x + 4 x x is to be defined to make continuous at x = 0, then the defined function should be
- f(x) = cases x^2 2 , & if 0 x 1 [1mm] 2x^2 - 3x + 3 2 , & if 1 < x 2 cases is
- If f(x) = cases x^3 + x^2 - 16x + 20 (x - 2)^2 , & x 2 [1mm] k, & x = 2 cases is continuous at x = 2, then the value of k is
- If f : R A is defined by f(x) = cases 2 x - 2x 2x x , & if x 0 [1mm] a, & if x = 0 cases then the value of a so that f is...
- The continuity of the function f, where f is defined by f(x) = cases -2, & if x -1 2x, & if -1 < x 1 2, & if x > 1 cases for
- The function f(x) = 9 - x^2 is continuous at
- The function f(x) = [x] is not continuous at which point in the interval [-1, 2)?
- Find the value of k, if f(x) is continuous at x = 0, where f(x) = cases xe^x + x 3x , & x 0 [1mm] k, & x = 0 cases
- If f(x) = ( 3x + 2 2 - 5x )^ 1 x , for x 0, is continuous at x = 0. Then f(0) is
- If f(x) = cases (1 + x) - (1 - x) x , & when x 0 [1mm] 3, & when x = 0 cases is
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