Question

If lim x→0 f(x)/x^2=9 Evaluate the Following
a)lim f(x)
x→0
b)Lim f(x)/x
x→0

Answer 1

There must be many functions f that would have the given limit.
Suppose we take f(x)=9x², then lim x→0 f(x)/x²=9.

Now, lim x→0 f(x) = lim x→0 9x² = 0.

I think it is easy to see what lim x→0 f(x)/x will be.