Calculus Topics

Given the region bounded by y 2x 3 1 y 8x 1 and x 0 Sketch this region using the window size of 0 3 2 17

Without using a calculator find all the solutions of 1 2 where t cos t

Give the exact values of the sine and cosine of the special angles listed below sin 6 5 cos 6 sin 0 cos 0 11 cos IM sin 7 7 6 11 11

Without using a calculator find all the solutions of 1 3 where t T tan t

Find exact function values No decimals If undefined answer DNE a 117 6 sin 77 4 COS tan 57 4

use matrix inversion to solve the given linear system x y 2 z 2 x 3 y 2 z 0 21 4x 5y 5z 3 22 2x 6y 5z 4 2x 3y 62 9 x 4y 4z 1

If f x 9x 3 sin z 3 cos z then f x 9 9 3 Round your answer to the nearest hundredth 3 cos z cos z 3 sin z o and f 4

Determine the derivative of h t 3 cos t 4 sin t L A

Use the Table of Integrals in the back of your Cextbook to evaluate the integral 1 81 sec 5t tan 5t 81 tan 5t 81 tan 51 C dt

1 074 Points MY NOTES DETA ASK YO Marginal Cost The following function C x 20

3 Find the exact length of the following curve a y ln 1 x 0 x 1 1 b y 1 e 2 0 x 1

If g x cos z then g x answer to the nearest hundredth sin 7 and g 5 1 56 x Round your

A ladder 10 ft long leans against a vertical wall If the lower end is being moved away from the wall at the rate of 6 ft sec how fast is the height of the top changing this will be a negative rate when the lower end is 6 feet from the wall The height of the top is changing at a rate of Simplify your answer ft sec 10 ft ft sec 10 ft when the lower end is 6 feet from the wall X y

In a trend that scientists attribute at least in part to global warming a certain floating cap of sea ice has been shrinking since 1980 The ice cap always shrinks in the summer and grows in winter Average minimum size of the ice cap in square miles can be approximated by A r In 2013 the radius of the ice cap was approximately 793 and was shrinking at a rate of approximately 4 1 mi yr How fast was the area changing at that time The area was changing at a rate of Round to the nearest integer as needed in 2013 mi yr mi yr yr mi mi yr mi yr

The volume of a cantaloupe is approximated by V The radius is growing at the rate of 0 4 cm week when the radius is 7 1 cm How fast is the volume changing at that moment The volume is changing at a rate of about Round to one decimal place as needed weeks cm week cm cm week cm week

Find the general solution using the power series 21