## Practice Final

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## Practice Final

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- Pages:
- 4
- School:
- Iowa State University
- Course:
- Math 165 - Calculus I

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Leader Course Instructor Date 12 09 Practice Final Supplemental Instruction Iowa State University Matt E Math 165 Kramer 12 09 10 Part 1 For the first part of the test do not use a calculator 1 Find y x ln a b c dy dx x x 4 x 6 x2 10 2 3 y x log 5 cos x 1 y x 2 sec 4 x x 2 d y x 4 x 1 4 sin t dt t Supplemental Instruction 1060 Hixson Lied Student Success Center v 294 6624 v www si iastate edu 2 Evaluate and simplify without using a calculator Don t rationalize denominator sin tan 1 4 3 Find the particular solution to the differential equation dy y tan x dx 4 Evaluate the following integrals a 1 c x 2 sin x 5 dx 1 y 2 e when that satisfies 1 x x ln x 2 dx b x 3 6 x 3 dx 2 x x 5 Part 2 You may now use a calculator on this part but don t go back and use it on Part 1 Show the work that leads to all answers 1 Find the volume of the largest right circular cylinder that will fit inside a sphere of radius 3ft 2 Water is draining from a large conical tank at a rate of 3 m3 s The cone is 10m tall and has a radius of 5m at the top i At what rate is the water level dropping when there is 1m depth of water left ii How long would it take to completely drain the tank if it were full 4 f x arctan x ln x 2 1 a On what closed intervals is f increasing b Find all critical points c Use the second derivative test if possible to classify each critical point as a max or min If the second derivative test fails use the first derivative test 5 A radioactive substance has a half life of 2000 years and there are initially 50 grams Let y t represent the amount in grams of the substance remaining after t years i Write a differential equation to describe this situation ii Solve your differential equation using the half life to find a particular solution y t iii How much of this substance is left after 9000 years Round to 3 decimal places

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