Chapter 1, Problem 27RE

In each part, a positive number $\in$ and the limit $L$ of a function $f$ at $a$ are given. Find a number $\delta$ such that $\left|f\left(x\right)-L\right|<\in \text{ if 0}<\left|x-a\right|<\delta$ .

(a) $\underset{x\to 2}{\lim }\left(4x-7\right)=1;\in =0.01$

(b) $\underset{x\to 3/2}{\lim }\frac{4x^2-9}{2x-3}=6;\in =0.05$

(c) $\underset{x\to 4}{\lim }{x}^2=16;\in =0.001$