91Ó°ÊÓ

Sketch reasonable graphs for the following. Pay particular attention to the concavity of the graphs. (a) The total revenue generated by a car rental business, plotted against the amount spent on advertising. (b) The temperature of a cup of hot coffee standing in a room, plotted as a function of time.

How many distinct roots can a polynomial of degree 5 have? (List all possibilities.) Sketch a possible graph for each case.

find a value of \(k\) making \(h(x)\) continuous on [0,5] $$h(x)=\left\\{\begin{array}{ll} e^{k x} & 0 \leq x<2 \\ x+1 & 2 \leq x \leq 5 \end{array}\right.$$

Use a graph of the function to decide whether or not it is invertible. $$f(x)=x^{3}+5 x+10$$

Use a graph to estimate each of the limits in Exercises \(19-28\) Use radians unless degrees are indicated by \(\theta^{\circ}\). $$\lim _{h \rightarrow 0} \frac{\cos (3 h)-1}{h}$$

Find a solution to the equation if possible. Give the answer in exact form and in decimal form. $$1=8 \cos (2 x+1)-3$$

Write a formula representing the function. The average velocity, \(v,\) for a trip over a fixed distance, \(d,\) is inversely proportional to the time of travel, \(t\)

find a value of \(k\) making \(h(x)\) continuous on [0,5] $$h(x)=\left\\{\begin{array}{ll} 0.5 x & 0 \leq x<1 \\ \sin (k x) & 1 \leq x \leq 5 \end{array}\right.$$

Put the functions in the form \(P=P_{0} e^{k t}\). $$P=4(0.55)^{t}$$

Use a graph to estimate each of the limits in Exercises \(19-28\) Use radians unless degrees are indicated by \(\theta^{\circ}\). $$\lim _{h \rightarrow 0} \frac{\sin (3 h)}{h}$$