Using Limit Laws to find f(x)

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...

tiny-tim

hi jmm12! welcome to pf!

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

jmm12

its in my post now, please help

HallsofIvy

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?

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 ?

jmm12

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

tiny-tim

that's correct!

but now prove it !

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?