Finding a limit at g(x). Analysis. Algebra of Limits.
Define by . Prove that g has a limit at 0 and find it.
In my course we are given only the definition of a limit, namely that has a limit at iff there exists a such that given any we have
for all .
We are also given the algebra of limits for Addition, Multiplication, and Division (given obvious constraints).
I cannot seem to find a clever way to write g(x) in the problem as a composition of two functions with either of these three operations. Any help would be appreciated.