Continuity and Differentiability questions
732 published questions with worked solutions.
- If f(x)= cases x-4 |x-4| +a, & for x<4 a+b, & for x=4 x-4 |x-4| +b, & for x>4 cases is continuous at x = 4, then
- Given that f(x)= cases 1- 4x x^ 2 & if x<0 a & if x=0 x 16+ x -4 & if x>0 cases is continuous at x = 0, then a=
- If f(x) = cases ( ^2 x )^ ^2 x , & for x 0 K + 1, & for x = 0 cases is continuous at x = 0, then value of K is
- If f(x)= x 2 -1, then on the interval [0, ] where [.] represents greatest integer function
- If the function f(x) is continuous on its domain [-2, 2] where f(x)= ax x +3, -2 x<0 = x+5, 0 x 1 = x^2+8 -b, 1<x 2, then 7a + b...
- The domain of the derivative of the functions f(x) = cases ^ -1 x, & if |x| 1 1 2 (|x|-1), & if |x| > 1 cases is given by
- The function f(x)=[x]^2-[x^2] (where, [x] is the greatest integer less than or equal to x), is discontinuous at
- f(x) = cases 1 - kx x^2 , & if x 0 x 16 + x - 4 , & if x > 0 cases is continuous at x = 0, then the value of k is
- The number of discontinuous of the greatest integer function f(x)=[x], x (- 72,100 )
- Let k be a non-zero real number. If f(x)= cases (e^x-1)^2 ( xk ) (1+ x4 ) ,&x 0 [2mm]12,&x=0 cases is a continuous function, then...
- Let S = t R f(x) = |x- | (e^ |x| - 1 ) |x| is not differentiable at t , then S is
- If f(x) = 4 x^4 [1 - x2 - x4 + x2 x4 ] is continuous at x = 0 then f(0) is
- If the function f(x) is continuous in 0 x , then the value of 2a + 3b is where f(x)= cases x+a 2 x & if 0 x 4 2x x+b & if 4 x 2 a...
- If the function f(x)= cases -2 x,& if x - 2 x+B,& if - 2 <x< 2 x,& if x 2 cases is continuous everywhere, then the values of A...
- The values of a and b, so that the function 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 for...
- The function defined by f(x)= cases x-4 |x-4| +a & if x<4 a+b & if x=4 x-4 |x-4| +b & if x>4 cases is continuous at x = 4, are
- If f(x) = [x] - [ x 4 ], x R where [x] denotes the greatest integer less than or equal to x, then
- Let the function f be defined by f(x)= x-|x| x , for x 0 and f(0)=2 then f is
- Let the function f(x) be defined as: f(x) = cases [ ( 4 + x ) ]^ 1 x , & x 0 k, & x = 0 cases If f(x) is continuous at x = 0,...
- If f(x)= cases x-3 |x-3| +a, & x<3 a+b, & x=3 |x-3| x-3 +b, & x>3 cases is continuous at x=3, then the value of a-b is
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