Question

If limit of `f(x)=3/2` and `g(x)=1/2` as `x->c`, what the limit of `f(x)g(x)` as `x->c`?

Answer 1

`lim_(xrarrc) {f(x)g(x)} =3/4`

Explanation:

This is one of the basic properties of limits:
`lim_(xrarrc) {f(x)g(x)} = {lim_(xrarrc)f(x)}{ lim_(xrarrc) g(x) }`

We are told that:
`lim_(xrarrc)f(x)=3/2`; and `lim_(xrarrc) g(x) =1/2`

Hence,
`lim_(xrarrc) {f(x)g(x)} = 3/2*1/2=3/4`