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 $\lim_{x\rightarrow \infty }e^x/p(x)=1$?

For any polynomial $P$, the limit $$\lim_{x\to\infty}\frac{e^x}{P(x)}$$ is equal to plus or minus $\infty$ (depending on the sign of the leading coefficient of $P$). This statement does not change just because you took the polynomial approximation for $e^x$ as your polynomial $P$.
