1. Provide an example of a function f that is continuous at a = 2 but not differentiable at a = 2.

Question

2. Provide an example of a function g that is differentiable at a = 3 but does not have a limit at a = 3.

Thanks!

Answer 1

f(x) = |x-2|

Answer 2

for the 2nd part, if a function is differentiable, it is continuous. Hence it has a limit at every point.