User:Egm6341.s11.team1.arm/HW1

Part (A)
Employ L'Hopital's Rule,

Define g and h as follows:

Therefore,

Problem 2
The Taylor series can be constructed from the well-known Taylor series for $$e^x$$ at $$ x = 0 $$ (Atkinson 1-1-4).

Subtracting one from this expression and dividing by $$x$$:

Therefore: