Using Limit Laws to Solve for f(x)

[jmm12]

Homework Statement

lim ( f(x)/(x²) )= 8
x→0

Then what is...

a)lim ( f(x) )
x→0

b)lim ( f(x)/x )
x→0

Homework Equations

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 don't know...

 

[tiny-tim]

welcome to pf!

hi jmm12! welcome to pf!

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

 

[jmm12]

hi jmm12! welcome to pf!

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

its in my post now, please help

 

[HallsofIvy]

The only thing in your post is

tried separating the limits
(lim x→0 f(x))(lim x→0 1/(x^2)) = 8

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?