Using Limit Laws to find f(x)


by jmm12
Tags: limits
jmm12
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#1
Feb1-12, 03:40 PM
P: 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...
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tiny-tim
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#2
Feb1-12, 03:43 PM
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hi jmm12! welcome to pf!
tell us what you think (and why), and then we'll comment!
jmm12
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#3
Feb1-12, 03:58 PM
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Quote Quote by tiny-tim View Post
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
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Feb1-12, 04:12 PM
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Using Limit Laws to find f(x)


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
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#5
Feb1-12, 04:15 PM
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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
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#6
Feb1-12, 04:20 PM
P: 4
so if the numerator has to be zero too..
then the lim x->0 f(x) is zero??????????
tiny-tim
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#7
Feb1-12, 04:22 PM
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that's correct!
but now prove it !
jmm12
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#8
Feb1-12, 04:30 PM
P: 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?


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