Continuity and Differentiability questions
732 published questions with worked solutions.
- For what value of k, the function f(x) = cases x |x| + 2x^2 , & x 0 k, & x = 0 cases is continuous at x = 0?
- The set of points of discontinuity of the function f(x) = _ n (2 x)^ 2n 3^n - (2 x)^ 2n is given by
- The function f(x) = ( 2x)^ ^2 2x is not defined at x = 4 . The value of f( /4), so that f is continuous at x = /4, is
- The values of a, b and c which make the function f(x) = cases (a + 1)x + x x , & x < 0 [1mm] c, & x = 0 [1mm] x + bx^2 - x bx^...
- If y = 1 t^2 - t - 6 and t = 1 x - 2 , then the values of x, then which make the function y discontinuous are?
- Let f(x) = cases ^2 x - ^2 x - 1 x^2 + 4 - 2 , & x 0 [1mm] a, & x = 0 cases , then the value of a in order that f(x) may be...
- Let f(x) = cases 1 - 4x x^2 , & if x < 0 [1mm] a, & if x = 0 [1mm] x 16 + x - 4 , & if x > 0 cases for what value of a, f is...
- If f(x) = 2x + A x + B x x^3 is continuous at x = 0, then the values of A, B and f(0) are
- f(x) = cases |x| + 3, & if x -3 -2x, & if -3 < x < 3 6x + 2, & if x 3 cases is
- The function f given by f(x) = cases e^ 1/x - 1 e^ 1/x + 1 , & if x 0 [1mm] 0, & if x = 0 cases is
- Which of the following is not continuous for all x?
- Let f(x) = x^3 + x be function and g(x) = cases f(|x|), & x 0 f(-|x|), & x < 0 cases then
- The jump of the function at the point of the discontinuity of the function f(x) = 1 - k^ 1/x 1 + k^ 1/x (k > 0) is
- If the function f(x) = cases x + a^2 2 x, & 0 x < 4 x x + b, & 4 x < 2 b 2x - a x, & 2 x cases is continuous in the interval [0,...
- If f(x) = cases x, & if x is rational -x, & if x is irrational cases then
- If f(x) = cases ( x + 3 x)^ 5 cosec x , & x ( - 2 , 2 ) - 0 , & x = 0 cases is continuous at x = 0, then will be
- Let f(x) = cases 1 + x^2 , & x < 3 3 x - 1, & 3 x < 4 [x], & 4 x < 5 |1 - x|, & x 5 cases , where [x] is the greatest integer x....
- The value of f(0), so that the function f(x) = a^2 - ax + x^2 - a^2 + ax + x^2 a + x - a - x becomes continuous for all x, is...
- The function f(x) = x - |x - x^2| is
- For the function f(x) = _e(1 + x) + _e(1 - x) x to be continuous at x = 0, the value of f(0) is
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