Question

Show by means of an example that
lim x-> a [f(x)g(x)] may exist even though neither lim x-> a f(x) nor lim x -> a g(x) exists.

Answer 1

Stewart Calculus?

Answer 2

I assigned this problem this semester ;)

Answer 3

Any chance you know the answer?

Answer 4

yes

Answer 5

many answers

Answer 6

infinity many

Answer 7

one example will do :)

Answer 8

you cannot count them on your fingers and toes is as much as i know
so therefore it is many
and possibly infinitely many

Answer 9

lol

Answer 10

never mind I got one I think

Answer 11

f(x)=1+sqroot(x) and g(x)= 1 - sqroot(x) when a <0?

Answer 12

Think of something really simple.

Answer 13

How about this function

f(x) = 0, for x =< 0
1, for x > 0

You should be home free now.