Continuity and Differentiability questions
732 published questions with worked solutions.
- Let [x] be the greatest integer . Then the number of points in the interval (–2, 1) where the function f(x) = |[x]|+ x-[x] is...
- Let [x] denote the greatest integer function and f(x) = max 1+x+[x], 2+x, x+2[x] , 0 x 2. Let m be the number of points in [0,...
- Let f(x) = cases x^2 ( 1 x ), & x 0 0, & x=0 cases , Then at x = 0
- Let ℝ denote the set of all real numbers. Define the function f : ℝ → ℝ by f(x) = cases 2 - 2x^2 - x^2 1 x & if x 0, 2 & if x =...
- f is defined in [-5, 5] as f(x) = x if x is rational and = -x is irrational. Then
- If f(x) = cases xe^ - ( 1 |x| + 1 x ) , & x 0 0, & x = 0 cases then f(x) is
- Let f(x) = 1 - x 4x - , x 4 , x [0, 2 ]. If f(x) is continuous in [0, 2 ], then f ( 4 ) is
- If f is a real-valued differentiable function satisfying |f(x) - f(y)| (x - y)^2, x, y R and f(0) = 0, then f(1) equals
- The set of points where f(x) = x 1 + |x| is differentiable is
- The function f : R 0 R given by f(x) = 1x - 2 e^ 2x - 1 can be made continuous at x = 0 by defining f(0) as
- Let f(x) = cases (x - 1) ( 1 x - 1 ), & if x 1 0, & if x = 1 cases . Then which one of the following is true?
- Let f(x) = x|x| and g(x) = x. Statement-1 : gof is differentiable at x = 0 and its derivative is continuous at that point....
- The value of p and q for which the function f(x) = cases (p + 1)x + x x , & x < 0 , & x = 0 x + x^2 - x x^ 3/2 , & x > 0 cases is...
- The value of k, for which the function f(x)= cases ( 45 )^ 4x 5x , & 0<x< 2 k+ 25, & x= 2 cases is continuous at x= 2, is
- If f(x)= 1+ x (1-x)^2 for x 1 is continuous at x=1, then f(1) is equal to
- Let K be the set of all real values of x, then function f(x)= |x|-|x|+2(x- ) |x| is not differentiable. Then the set K is
- If the function f(x) = cases ( 5x-8 8-3x )^ 3 2x-4 & if x 2 k & if x = 2 cases is continuous at x = 2, then k =
- If f(x) = x + x^2 + x^3 + + x^n - n x - 1 for x 1 is continuous at x = 1, then f(1) =
- Let a,b R (a 0). If the function f is defined as f(x)= cases 2x^2 a , & 0 x<1 [2mm] a, & 1 x< 2 [2mm] 2b^2-4b x^3 , & 2 x< cases...
- If f(x)= e^ x^2 - x x^2 , if is continuous at x=0, then f(0)=
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