Question about $e^x$ Let $ p(x)=1+x+x^2/2!+x^3/3!+....+x^n/n!$ where $n$ is  a large positive integer.Can it be concluded  that $\lim_{x\rightarrow \infty }e^x/p(x)=1$?

No.
$$\frac{e^x}{p(x)}=1+\frac{\sum\limits_{k=n+1}^\infty \frac {x^k}{k!}}{p(x)}\stackrel{x\to\infty}\to\infty$$
