Chapter 13.1, Problem 53E

(a)

To determine

To prove: The property $\underset{t\to a}{\lim }\left[u\left(t\right)+v\left(t\right)\right]=\underset{t\to a}{\lim }u\left(t\right)+\underset{t\to a}{\lim }v\left(t\right)$.

(b)

To determine

To prove: The property $\underset{t\to a}{\lim }cu\left(t\right)=c\underset{t\to a}{\lim }u\left(t\right)$.

(c)

To determine

To prove: The property $\underset{t\to a}{\lim }\left[u\left(t\right)\cdot v\left(t\right)\right]=\underset{t\to a}{\lim }u\left(t\right)\cdot \underset{t\to a}{\lim }v\left(t\right)$.

(d)

To determine

To prove: The property $\underset{t\to a}{\lim }\left[u\left(t\right)\times v\left(t\right)\right]=\underset{t\to a}{\lim }u\left(t\right)\times \underset{t\to a}{\lim }v\left(t\right)$.