Chapter A.5, Problem 4E

To determine

To prove: That $\underset{x\to c}{\lim }f\left(x\right)=f\left(c\right)$ for any polynomial function $f\left(x\right)=a_n{x}^n+a_{n-1}{x}^{n-1}+\cdots +a_{1}x+a_0$, using the fact $\underset{x\to c}{\lim }\left(k\right)=k$ for any number k and the result of exercises 1 to 3.