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AP Calculus AB: Continuity, Differentiability, Limit online Test


f(x) is Continuous and differentiable
f(x) is Continuous and not differentiable
f’(1)=-1
f’(1)=1
f’(1)=0


Continuous at x=0
Continuous in (-1,0)
Differentiable in (–1,1)
Constant function in [-1, 1]
All the above

Continuous at x=1
Continuous at x=3
Differentiable at x=1
Differentiable at x=2
Differentiable at x=3




I only
I and IV
II and III
IV only
II and IV


I and II are true
I and III are true
II and IV are true
III and IV are true
I and IV are true




Not continuous at x=2
Differentiable at x=2
Continuous but not differentiable at x=2
Not differentiable at x=2
Neither continuous nor differentiable at x=2





0
1
2
Does not exist
-2

f is continuous but not differentiable
f is differentiable but not continuous
f’ is continuous but not differentiable
f’ is continuous and differentiable
f’ is neither continuous nor differentiable
Description:

This test contains twenty questions on Continuity of functions, derivatives. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number. Wherever appeared, lnx represents the natural logarithm of x with base e. Sometimes, the options may not contain exact numerical value of an answer. In that case, select best approximation to the numerical value you got. After examining the form of the choices, decide the best of the choices given.

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