Chapter 1.2, Problem 42E

(a)

To determine

To calculate: The value of $\delta$ and the limit “L” using the function $\underset{x\to 4}{\lim }{x}^2+6$ and $\epsilon =0.01$, if $\left|f(x)-L\right|<\epsilon ,\text{then }0<\left|x-c\right|<\delta$.

(b)

To determine

To calculate: The value of $\delta$ and the limit “L” using the function $\underset{x\to 4}{\lim }{x}^2+6$ and $\epsilon =0.005$, if $\left|f(x)-L\right|<\epsilon ,\text{then}0<\left|x-c\right|<\delta$.