Problem 8
Solve for \(x\). $$ (x+3)^{4 / 3}=16 $$
Problem 8
Find the limit (if it exists). If it does not exist, explain why. $$ \lim _{x \rightarrow 3^{+}} \frac{|x-3|}{x-3} $$
Problem 8
Find the limit. $$ \lim _{x \rightarrow 3} \frac{2 x-5}{x+3} $$
Problem 9
Solve for \(x\). $$ e^{-2 x}=e^{5} $$
Problem 9
\( \text { Rate of Change } \) Each of the following is the slope of a line representing daily revenue \(y\) in terms of time \(x\) in days. Use the slope to interpret any change in daily revenue for a one-day increase in time. (a) \(m=400\) (b) \(m=100\) (c) \(m=0\)
Problem 9
Find the limit (if it exists). If it does not exist, explain why. $$ \lim _{x \rightarrow 3^{-}} f(x), \text { where } f(x)=\left\\{\begin{array}{ll} \frac{x+2}{2}, & x \leq 3 \\ \frac{12-2 x}{3}, & x>3 \end{array}\right. $$
Problem 9
In Exercises \(7-20,\) find the vertical asymptotes (if any) of the function. $$ g(t)=\frac{t-1}{t^{2}+1} $$
Problem 9
Find the limit. $$ \lim _{x \rightarrow \pi / 2} \sin x $$
Problem 10
Modeling Data The table shows the rate \(r\) (in miles per hour) that a vehicle is traveling after \(t\) seconds. $$ \begin{array}{|c|c|c|c|c|c|c|} \hline t & 5 & 10 & 15 & 20 & 25 & 30 \\ \hline r & 57 & 74 & 85 & 84 & 61 & 43 \\ \hline \end{array} $$ (a) Plot the data by hand and connect adjacent points with a line segment. (b) Use the slope of each line segment to determine the interval when the vehicle's rate changed most rapidly. How did the rate change?
Problem 10
Find the limit (if it exists). If it does not exist, explain why. $$ \lim _{x \rightarrow 2} f(x), \text { where } f(x)=\left\\{\begin{array}{ll} x^{2}-4 x+6, & x<2 \\ -x^{2}+4 x-2, & x \geq 2 \end{array}\right. $$
