Continuity and Differentiability questions
732 published questions with worked solutions.
- Let f : R R be defined by f(x) = cases 3x - x x^2 , & x 0 , & x = 0 cases . If f is continuous at x = 0, then is equal to
- If f(x) = cases 2x 5x , & when x 0 k, & when x = 0 cases is continuous at x = 0, then the value of k will be
- If f(x) = cases (e^ kx - 1)^2 x x^3 , & x 0 4, & x = 0 cases is continuous at x = 0, then k =
- The function 'f' is defined by f(x) = 2x - 1, of x > 2, f(x) = k if x = 2 and x^2 - 1, if x < 2 is continuous, then the value of...
- If f(x) = cases 1 - 4x x^2 , & when x < 0 [1mm] a, & when x = 0 [1mm] x (16 + x ) - 4 , & when x > 0 cases is continuous at x =...
- For the function f(x) = cases x^3 - a^3 x - a , & x a b, & x = a cases If f(x) is continuous x = a, then b is equal to
- If f(x) = 1 - x ( - 2x)^2 , when x 2 and f ( 2 ) = , then f(x) will be continuous function at x = 2 , when
- The function defined by f(x) = cases (x^2 + e^ 1 2 - x )^ -1 , & x 2 k, & x = 2 cases is continuous from right at the point x =...
- For the function f(x) = _e(1 + x) - _e(1 - x) x to be continuous at x = 0, the value of f(0), should be
- If f(x) = |x - 2|, then
- If f(x) = cases x^2 - 9 x - 3 , & if x 3 2x + k, & otherwise cases , is continuous at x = 3, then k =
- If f(x) = x^2 - 10x + 25 x^2 - 7x + 10 for x 5 and f is continuous at x = 5, then f(5) =
- If the function f(x) = cases ( x)^ 1 x , & x 0 k, & x = 0 cases is continuous at x = 0, then the value of k is
- f(x) = x ( /x) is continuous everywhere, then f(0) =
- If f(x) = cases x^2 + 3x - 10 x^2 + 2x - 15 , & when x -5 a, & when x = -5 cases is continuous at x = -5, then the value of 'a'...
- In order that the function f(x) = (x + 1)^ x is continuous at x = 0, f(0) must be defined as
- Let f(x) = cases x - x x - 4 , & x 4 [1mm] a, & x = 4 cases The value of a so that f(x) is continuous at x = 4 , is
- The value of f at x = 0 so that the function f(x) = 2^x - 2^ -x x , x 0 is continuous at x = 0, is
- The function f(x) = 1 - x + x 1 + x + x is not defined at x = . The value of f( ), so that f(x) is continuous at x = , is
- If f(x) = cases x + , & x < 3 4, & x = 3 3x - 5, & x > 3 cases is continuous at x = 3, then =
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