The function can't be , because isn't surely bounded by for all , but if you rewrite:
and you know then the limit is ...
Suppose 0≤ f(x) ≤1 for all x, find
lim x⁴ f(x)
x→0.
This is exactly how the question is presented in my manual and I am not sure if it is trying to say that the function is x⁴ or something else. Also, I am not sure what relevance the first part of the question has to finding the limit. I believe it is representing the range, although I don't know what that means as far as limits go. Thank-you for your help.
Thank-you for your quick reply.
I am still a little unclear as to the part which states:
0≤ f(x) ≤1 for all x.
Does this represent the range of f(x)?
I understand that if the limit of
lim x⁴
x→0
is 0 that multiplying this by the limit of f(x) will yield a limit of 0. I am just wondering about the relevance of the range stated and whether that should affect my solution. Thank-you.