Continuity and Differentiability questions
732 published questions with worked solutions.
- Let f(x) = 1 + | x|. Then
- Let f : R R be a function. Define g : R R by g(x) = |f(x)| for all x. Then g is
- Let f: R R be a function defined by f(x) = x, x^3 . The set of all points where f(x) is not differentiable is
- The left-hand derivative of f(x) = [x] x at x = k, where k is an integer and [x] = greatest integer not greater than x, is
- Which of the following functions is differentiable at x = 0?
- The domain of the derivative of the function f(x) = cases ^ -1 x & for |x| 1 [2pt] 12(|x| - 1) & for |x| > 1 cases is
- In the following [x] denotes the greatest integer less than or equal to x. Match the functions in **Column I** with the...
- Let f and g be real-valued functions defined on interval (-1, 1) such that g''(x) is continuous, g(0) 0, g'(0) = 0, g''(0) 0 and...
- Let f: R R be a function such that f(x + y) = f(x) + f(y), , x, y R . If f(x) is differentiable at x = 0 then
- If the function g(x) = cases k x+1 , & 0 x 3 + 2, & 3 < x 5 cases is differentiable, then the value of k + m is
- If f(x) is a differentiable function in the interval (0, ) such that f(1) = 1 and _ t x t^2f(x)-x^2f(t) t-x = 1, for each x > 0,...
- If the function f(x) = cases -x, & x<1 a+ ^ -1 (x+b), & 1 x 2 cases is differentiable at x = 1, then ab is equal to
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