Chapter 4.7, Problem 8E

(a)

To determine

To prove: The function $f\left(x\right)=x^2-3\text{at }a=2$ is continuous at the given point a.

(b)

To determine

To prove: The function $f\left(x\right)=3x^2+1ata=1$ is continuous at the given point a.

(c)

To determine

To prove: The function $f\left(x\right)=\left|x-3\right|ata=3$ is continuous at the given point a.

(d)

To determine

To prove: The function $f\left(x\right)=\{\begin{array}{cc}2x+5& x\ge 2\\ 1+4x& x<2\end{array}ata=3$ is continuous at the given point a.