Continuity and Differentiability questions
732 published questions with worked solutions.
- The set of all points, where the function f(x)= 1-e^ -x^2 is differentiable, is
- If f(x)=x ( x - x+1 ), then f(x) is
- Let g be the greatest integer function. Then the function f(x)=(g(x))^2-g(x^2) is discontinuous at
- Consider the function f(x)= cases x^2 |x| & x 0 0 & x=0 cases . What is f'(0) equal to?
- If f(x)= x^2-9 x^2-2x-3 , x 3 is continuous at x=3, then which one of the following is correct?
- Consider the function f(x)= cases 2x 5x & if x 0 2 15 & if x=0 cases Which one of the following is correct in respect of the...
- For the function f(x)=|x-3|, which one of the following is **not** correct?
- If the function f(x)= 2x- ^ -1 x 2x+ ^ -1 x is continuous at each point in its domain, then what is the value of f(0)?
- If y=| x|^ |x| , then what is the value of dy dx at x=- 6 ?
- Consider the following statements in respect of the function f(x)= ( 1 x ) for x 0 and f(0)=0 : 1. _ x 0 f(x) exists 2. f(x) is...
- For what value of k is the function f(x)= cases 2x+ 1 4 , & x<0 , & x=0 (x+ 1 2 )^2, & x>0 cases continuous?
- If f(x)= x x , where x R , is to be continuous at x=0, then the value of the function at x=0
- Consider the following statements for f(x)=e^ -|x| : 1. The function is continuous at x=0. 2. The function is differentiable at...
- Consider the following statements in respect of the function y=[x], x (-1, 1) where [.] is the greatest integer function : 1. Its...
- Let y=[x+1], -4<x<-3 where [.] is the greatest integer function. What is the derivative of y with respect to x at x=-3 5?
- Consider the following in respect of the function f(x)=10^x : 1. Its domain is (- , ) 2. It is a continuous function 3. It is...
- If f(x) is differentiable at x=a, then consider the following statements : I. f(x) is continuous at x=a II. _ x a f(x)=f(a) Which...
- What is the derivative of x |x| with respect to x, where x<0?
- Consider the following statements in respect of the function f(x)=[3x], where [ ] is the greatest integer function : I. f(x) is...
- Let f(x)=p|x|+q, where p and q are real constants. If f'(x) exists at x=0, then what is the value of p?
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