Mathematics

Problem

For a limit of the form

\displaystyle\lim_{x\to c}\frac{f(x)}{g(x)}

to be classified as an indeterminate expression of type

0/0

, which of the following conditions must be satisfied at

x=c

? a)

f(c)=0

and

g(c)\neq 0

f(c)\neq 0

and

g(c)=0

f(c)=0

and

g(c)=0

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

and

\displaystyle\lim_{x\to c}g(x)=0