Mathematics

Problem

A function

f

satisfies

|f(x)|\le x^{4}

for all

x

in an open interval containing

0

. Which of the following must be true? a)

\displaystyle \lim_{x\to 0} f(x)=1

\displaystyle \lim_{x\to 0^{+}} f(x)=0\text{ but }\lim_{x\to 0^{-}} f(x)\text{ may differ}

\displaystyle \lim_{x\to 0} f(x)=0

\displaystyle \lim_{x\to 0} f(x)\text{ does not exist}