Using Limit Laws to find f(x)

1. Feb 1, 2012

jmm12

1. The problem statement, all variables and given/known data
lim ( f(x)/(x2) )= 8
x→0

Then what is...

a)lim ( f(x) )
x→0

b)lim ( f(x)/x )
x→0

2. Relevant equations

3. The attempt at a solution

tried separating the limits
(lim x→0 f(x))(lim x→0 1/(x2)) = 8

but the lim x→0 1/(x2) is ∞ ... soooo i dont know...

Last edited: Feb 1, 2012
2. Feb 1, 2012

tiny-tim

welcome to pf!

hi jmm12! welcome to pf!

tell us what you think (and why), and then we'll comment!

3. Feb 1, 2012

jmm12

Re: welcome to pf!

4. Feb 1, 2012

HallsofIvy

Staff Emeritus
The only thing in your post is
and that is NOT in general true. Since the denominator goes to 0, what must the numerator go to in order that this limit exist?

5. Feb 1, 2012

tiny-tim

draw the graph of 1/x2 (near zero) …

roughly what do you think the graph of f(x) will have to look like if f(x)/x2 -> 8 ?

6. Feb 1, 2012

jmm12

so if the numerator has to be zero too..
then the lim x->0 f(x) is zero??????????

7. Feb 1, 2012

tiny-tim

that's correct!

but now prove it !

8. Feb 1, 2012

jmm12

what would lim f(x) / x as x->0 be then..

if (lim x->0 f(x)) / (lim x->0 x)

0/0...or dne?