# Using Limit Laws to find f(x)

1. ### jmm12

4
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. ### tiny-tim

26,041
welcome to pf!

hi jmm12! welcome to pf!

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

3. ### jmm12

4
Re: welcome to pf!

4. ### HallsofIvy

40,810
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. ### tiny-tim

26,041
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. ### jmm12

4
so if the numerator has to be zero too..
then the lim x->0 f(x) is zero??????????

7. ### tiny-tim

26,041
that's correct!

but now prove it !

8. ### jmm12

4
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?