Continuity and Differentiability questions
732 published questions with worked solutions.
- Function f(x) = cases x x + 2 x, & x 0 3, & x = 0 cases is
- If f(x) = cases (1 + 2ax) - (1 - bx) x , & x 0 k, & x = 0 cases is continuous at x = 0, then k is equal to
- If f(x) = (a + x)^2 (a + x) - a^2 a x , x 0; then the value of f(0) so that f is continuous at x = 0 is
- If f(x) = cases (a + 1)x + x x , & x < 0 [1mm] 1 2 , & x = 0 [1mm] x^ 3/2 + 1 2 , & x > 0 cases is continuous at x = 0, then the...
- If f(x) = cases 2x + 1, & x 1 3 - kx^2, & x > 1 cases is continuous at x = 1, then the value of k is
- If f(x) = cases x^2 - 1 x + 1 , & when x -1 -2, & when x = -1 cases , then
- Function f(x) = (1 + x a )^ 1 x is continuous at x = 0 if f(0) equals
- If the function f(x) = cases k x - 2x , & when x 2 [1mm] 3, & when x = 2 cases be continuous at x = 2 , then k =
- If f(x) = 3^x + 3^ -x - 2 x^2 for x 0 is continuous at x = 0, if f(0) is equal to
- If f(x) = cases x x , & x 0 [1mm] 1, & x = 0 cases , then f(x) is:
- If f is continuous at x = 0 where f(x) = (e^ 3x - 1) x x^2 , x 0, then f(0) =
- Let f(x) = cases x - 4 |x - 4| + a, & x < 4 [1mm] a + b, & x = 4 [1mm] x - 4 |x - 4| + b, & x > 4 cases , then f(x) is continuous...
- The value of f(0), so that the function f(x) = (27 - 2x)^ 1 3 - 3 9 - 3(243 + 5x)^ 1 5 , (x 0) is continuous, is given by
- If f(x) = cases x + a 2 x, & 0 < x < 4 2x x + b, & 4 x 2 a 2x - b x, & 2 < x cases Is continuous at x = 4 , then a - b is equal to
- If f(x) = cases 4 - 3x, & 0 < x 2 2x - 6, & 2 < x 3 x + 5, & 3 < x 6 cases then f(x) is
- If f(x) = (2^x - 1)^2 x (1 + x) for x 0, = 4 for x = 0
- If f(x) = cases |x|, & x < 0 x, & 0 x 1 1, & x > 1 cases , then f(x) is discontinuous at
- The point of discontinuity of the function f(x) = 1 + 5x 1 - 4x is:
- If f(x) = cases x x, & 0 < x 2 2 ( + x), & 2 < x < cases , then:
- If f(x) = x - [x], where [x] = greatest integer x, then f is discontinuous at
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