1. The problem statement, all variables and given/known data lim ( f(x)/(x^{2}) )= 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/(x^{2})) = 8 but the lim x→0 1/(x^{2}) is ∞ ... soooo i dont know...
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?
draw the graph of 1/x^{2} (near zero) … roughly what do you think the graph of f(x) will have to look like if f(x)/x^{2} -> 8 ?