Continuity and Differentiability questions
732 published questions with worked solutions.
- Let f(x) = + |x| + |x|^2, where , , are real constants. Then f'(0) exists if
- If f(x) = [x] |x| , x 0, where [ ] denotes the greatest integer function, then f'(1) is
- If f(x) = | 2x| then f' ! ( 4 +0 ) is equal to
- If f(x) = [x] then f'(1-0) is equal to
- Let f(x) = [x^2] - [x]^2, where [ ] denotes the greatest integer function. Then
- Let f(x) = [ x + x], 0 < x < 2 , where [x] denotes the greatest integer less than or equal to x. The number of points of...
- Let f(x) = x - |x - x^2|, x [-1,1]. Then the number of points at which f(x) is discontinuous is
- Let f(x)= cases 1+x^2 , & x< 3 3 ,x-1, & 3 x<4 [x], & 4 x<5, where [x] is the greatest integer x |1-x|, & x 5 cases The number of...
- Let f(x)= _0^x t 1t ,dt. Then the number of points of discontinuity of the function f(x) in the open interval (0, ) is
- Let f:[0,1] [0,1] be a continuous function. Then
- Let f(x) be a continuous function defined for 1 x 3. If f(x) takes rational values for all x and f(2)=10 then the value of f(1.5)...
- If f(x)=e^ -1/x^2 , x 0, and f(0)=0 then f'(0) is
- Let f(x)= x, g(x)=[x+1] and g f(x) =h(x), where [ ] is the greatest integer function. Then h' ! ( 2 ) is
- Let f(x)=[x], g(x)=|x| and f g(x) =h(x), where [ ] is the greatest integer function. Then h'(-1) is
- The number of values of x [0,2] at which the real function f(x)= |x- 12 |+|x-1|+ x is not finitely differentiable is
- Let f(x)=[n+p x], x (0, ), n Z , p is a prime number and [x]= the greatest integer less than or equal to x. The number of points...
- Let f(x)= cases (x-1)^2 1 x-1 -|x|, & x 1 -1, & x=1. cases The set of points where f(x) is not differentiable is
- Let f(x)= 1- x 2x , x 2 . If f(x) is continuous at x= 2 then f ! ( 2 ) should be
- A function f(x) is defined as below f(x)= ( x)- x x^2 , x 0 and f(0)=a. f(x) is continuous at x=0 if a equals
- Let f(x)= cases 1- x 4x- , & x 4 and x [0, 2 ) [2mm] , & x= 4 cases If f(x) is continuous in [0, 2 ) then is
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