Chapter 2.3, Problem 57E

(a)

To determine

Show that for each $\delta >0$, there is a value of x such that

$\left|f\left(x\right)-2\right|<2$ whenever $\left|f\left(x\right)-2\right|\ge \frac{1}{2}$

Show that the value of the limit $\underset{x\to 1}{\lim }f\left(x\right)\ne 2$.

(b)

To determine

Show that the limit $\underset{x\to 1}{\lim }f\left(x\right)\ne 1$.

(c)

To determine

Show that the limit $\underset{x\to 1}{\lim }f\left(x\right)\ne 1.5$.