Continuity and Differentiability questions
732 published questions with worked solutions.
- Let f(x)=( x)^ 1 -2x , x 2 . If f(x) is continuous at x= 2 then f ! ( 2 ) is
- Let f(x)= 1x, x 0. Then f(x) can be continuous at x=0
- If f(x)= cases px^2-q, & x [0,1) x+1, & x (1,2] cases and f(1)=2 then the value of the pair (p,q) for which f(x) cannot be...
- If f(x)=x, x 1, and f(x)=x^2+bx+c, x>1, and f'(x) exists finitely for all x R then
- If f(x)= cases e^x, & x<2 a+bx, & x 2 cases is differentiable for all x R then
- Let f(x)=x-|x|. Then
- If f(x)=[x]+ [x+ 12 ], where [ ] denotes the greatest integer function, then
- At x=0, the function y=e^ -|x| is
- A function f(x) is defined as follows: f(x)= cases -x^2, & x 0 5x-4, & 0<x 1 4x^2-3x, & 1<x 2 3x+4, & x>2 cases
- The function f(x)= 1x- 2 e^ 2x -1 , x 0, is continuous at x=0. Then
- The function f(x)=|x^2-3x+2|+ |x| is not differentiable at x=
- Let f(x) be defined as follows: f(x)= cases x^6, & x^2>1 x^3, & x^2 1. cases Then f(x) is
- Let f(x)= cases x, & x 0 - x, & x<0. cases Then f(x) is
- If f(x)= _ n=0 ^ n a_n|x|^n, where a_i's are real constants, then f(x) is
- Let [x] denote the greatest integer less than or equal to x. Now g(x) is defined as below: g(x)= cases [f(x)], & x (0, 2 ) ( 2 ,...
- Let f(x)= (x)+ (x) and '(a), '(a) are finite and definite. Then
- Let f(x)=x+|x|. Then f(x) is
- Let f(x)= _ n 1-x^n 1+x^n . Then
- Let f(x)=1-| x| for all x R. Then
- Let f(x)=[ ^2x], where [ ] denotes the greatest integer function. Then
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