91Ó°ÊÓ

Use analytical and/or graphical methods to determine the largest possible sets of points on which the following functions have an inverse.erated integral as an iterated integral with the indicated order of integration. $$f(x)=1 /(x-5)$$

Evaluating trigonometric functions Evaluate the following expressions using a unit circle. Use a calculator to check your work. All angles are in radians. $$\tan (15 \pi / 4)$$

Evaluating trigonometric functions Evaluate the following expressions using a unit circle. Use a calculator to check your work. All angles are in radians. $$\cot (-13 \pi / 3)$$

Graph each function with a graphing utility using the given window. Then state the domain and range of the function. $$f(x)=\left(9-x^{2}\right)^{3 / 2} ; \quad[-4,4] \times[0,30]$$

Graph each function with a graphing utility using the given window. Then state the domain and range of the function. $$g(t)=\frac{1}{1+t^{2}} ; \quad[-7,7] \times[0,1.5]$$

Evaluating trigonometric functions Evaluate the following expressions using a unit circle. Use a calculator to check your work. All angles are in radians. $$\sec (7 \pi / 6)$$

Determine an appropriate domain of each function. Identify the independent and dependent variables. A stone is thrown vertically upward from the ground at a speed of \(40 \mathrm{m} / \mathrm{s}\) at time \(t=0 .\) Its distance \(d\) (in meters) above the ground (neglecting air resistance) is approximated by the function \(f(t)=40 t-5 t^{2}\).

Evaluating trigonometric functions Evaluate the following expressions using a unit circle. Use a calculator to check your work. All angles are in radians. $$\cot (-17 \pi / 3)$$

a. Find the inverse of each function (on the given interval, if specified) and write it in the form \(y=f^{-1}(x)\) b. Verify the relationships \(f\left(f^{-1}(x)\right)=x\) and \(f^{-1}(f(x))=x\) $$f(x)=2 x$$

Suppose that it costs 5 e per minute to park at the airport with the rate dropping to 3 e per minute after 9 p.M. Find and graph the cost function \(c(t)\) for values of \(t\) satisfying \(0 \leq t \leq 120 .\) Assume that \(t\) is the number of minutes after 8 P.M.