# Using Limit Laws to find f(x)

by jmm12
Tags: limits
 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...
 Sci Advisor HW Helper Thanks P: 26,148 hi jmm12! welcome to pf! tell us what you think (and why), and then we'll comment!
P: 4
 Quote by tiny-tim hi jmm12! welcome to pf! tell us what you think (and why), and then we'll comment!

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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?
 Sci Advisor HW Helper Thanks P: 26,148 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 ?
 P: 4 so if the numerator has to be zero too.. then the lim x->0 f(x) is zero??????????
 Sci Advisor HW Helper Thanks P: 26,148 that's correct! but now prove it !
 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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