Chapter 13.1, Problem 53E

To determine

(a)

To prove:

$\underset{t\to a}{\lim }\left[u\left(t\right)+v\left(t\right)\right]=\underset{t\to a}{\lim }u\left(t\right)+\underset{t\to a}{\lim }v\left(t\right)$

To determine

(b)

To prove:

$\underset{t\to a}{\lim }cu\left(t\right)=c\underset{t\to a}{\lim }u\left(t\right)$

To determine

(c)

To prove:

$\underset{t\to a}{\lim }\left[u\left(t\right)·v\left(t\right)\right]=\underset{t\to a}{\lim }u\left(t\right)·\underset{t\to a}{\lim }v\left(t\right)$

To determine

(d)

To prove:

$\underset{t\to a}{\lim }\left[u\left(t\right)\times v\left(t\right)\right]=\underset{t\to a}{\lim }u\left(t\right)\times \underset{t\to a}{\lim }v\left(t\right)$