Continuity and Differentiability questions
732 published questions with worked solutions.
- The set of all points, where the derivative of the function f(x)= x 1+|x| exits, is
- If f(x)= cases a 2 (x-|x|), & for x<0 0, & for x=0 bx^ 2 ( 1 x ), & for x>0 cases is continuous at x = 0, then
- If f(x)=ax^2+bx+1, if |2x-3| 2 =3x+2, if 1 2 <x< 5 2 is continuous on its domain, then a+b has the value
- Given f(x) = cases 1 - 4x x^2 , & if x < 0 a, & if x = 0 x 16 + x - 4 , & if x > 0 cases If f(x) is continuous at x = 0, then...
- If f(x) is continuous at x=0, where f(x)= 8^x-2^x k^x-1 , for x 0 and f(0) = 2, then the value of k is …..
- If f(x)= cases (8-2x)^ 1 3 -2 3-(243+5x)^ 1 5 , & if x 0 k, & if x=0 cases is continuous at x = 0, then k =
- If f(x) is continuous on its domain [-2, 2], where f(x)= cases ax x +3, & -2 x<0 2x+7, & 0 x 1 x^2+8-b , & 1<x 2 cases then the...
- The function f(t) = 1 t^2 + t - 2 where t = 1 x-1 is discontinuous at
- If y = (x - x) + (x - x) + (x - x) + , then dy dx =
- The function f(x)=[x] ( 2x-1 2 ) , where [ ] denotes the greatest integer function, is discontinuous at
- The value of f(0) so that the function f(x)= (256-8x)^ 14 -4 16-4(64+3x)^ 13 , x 0, is continuous at x = 0, is
- If the function f is continuous at x=1, where f(x)= 1+ ( x) (1-x)^2 , for x 1, then the value of f(1) is ….
- Let f:[-1,3] IR be defined as f(x)= cases |x|+[x], & -1 x<1 x+|x|, & 1 x<2 x+[x], & 2 x<3 cases where [t] denotes the greatest...
- If the function f is continuous at x= , where f(x)= 1- [7(x- )] 5(x- )^2 , for x , then f( )=
- If the derivative of the function f(x)= cases ax^2+b & if x<-1 bx^2+ax+4 & if x -1 cases is continuous everywhere then
- If the function f(x) = 4 2 ( 3x + x) 2 2x 3x 2 + 5x 2 - 3x 2 , for x 2 is continuous at x = 2 , then the value of f ( 2 ) is...
- Which of the following function is discontinuous at x = 0?
- If f(x)= 3^x+3^ -x -2 x (1+x) for x 0, is continuous at x=0, then the value of f(0) is equal to ...
- The number of point / points where the function f(x)= 1 x^2-5|x|+6 is discontinuous is…
- If g(x)=(x^2+2x+1) f(x) such that f(0)=5 and _ x 0 f(x)-5 x =4 then g'(0)=
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