Give an example of:
(i) A function which is defined at a point and have a vertical asymptote at the same
point.
Answer the following question by True or False, and justify your answer. If f(x) is differentiable and f(x) = f(−x) then f′(x) = f′(−x).
f(x) is differentiable twice, show that
f′′(x) = lim f(x+2h)−2f(x+h)+f(x)
h→0