Answer
a. $-21$
b. $49$
c. $0$
d. $1$
e. $1$
f. $7$
g. $-7$
h. $-\frac{1}{7}$
Work Step by Step
Given $\lim_{t\to t_0}f(t)=-7$ and $\lim_{t\to t_0}g(t)=0$
a. $\lim_{t\to t_0}3f(t)=3\lim_{t\to t_0}f(t)=3\times(-7)=-21$
b. $\lim_{t\to t_0}(f(t))^2=(-7)^2=49$
c. $\lim_{t\to t_0}f(t)g(t)=-7\times0=0$
d. $\lim_{t\to t_0}\frac{f(t)}{g(t)-7}=\frac{-7}{0-7}=1$
e. $\lim_{t\to t_0}cos(g(t))=cos0=1$
f. $\lim_{t\to t_0}|f(t)|=|-7|=7$
g. $\lim_{t\to t_0}(f(t)+g(t))=-7+0=-7$
h. $\lim_{t\to t_0}\frac{1}{f(t)}=-\frac{1}{7}$
