## Using Limit Laws to find f(x)

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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## 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?
 Blog Entries: 27 Recognitions: Gold Member Homework Help Science Advisor 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 ?
 so if the numerator has to be zero too.. then the lim x->0 f(x) is zero??????????
 Blog Entries: 27 Recognitions: Gold Member Homework Help Science Advisor that's correct! but now prove it !
 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?

 Tags limits