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04_Midterm2-Sample - t 2 feet(a(6 points What is the...

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University of California, Riverside Department of Mathematics Midterm 2 Mathematics 9A - First Year of Calculus Sample 4 Instructions: This exam has a total of 100 points. You have 50 minutes. You must show all your work to receive full credit You may use any result done in class. The points attached to each problem are indicated beside the problem. You are not allowed to use books, notes, or calculators. Answers should be written as p 2 as opposed to 1 : 4142135 ::: . 1. Find the following derivatives using the pertinent rules and knowledge of a basic list of derivatives. (a) (6 points) d dx (1 + 4 x ) 5 (2 + x + x 2 ) 8 ± (b) (7 points) d dx ² x 2 + 2 x 4 3 x 2 + 1 ³ (c) (7 points) d dx ² 3 p x 1 3 p x ³ 2. (20 points) Find dy dx for a function y relation, 4 cos x sin y = 1 . 3. A ball is projected upward from the ground. Assuming that the only expression, h = 10 t 16
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Unformatted text preview: t 2 feet. (a) (6 points) What is the initial velocity of the ball? 1 (b) (7 points) What is the maximum height reached by the ball? (c) (7 points) Is the acceleration of the ball constant or not? Justify your answer. 4. (20 points) Legend has it the great pyramid of Giza was constructed in 20 years. Its base is square with sidelength 230 metres and its height is 150 metres. Assuming that slaves who constructed the pyramid increased the volume of the pyramid at a constant rate over the twenty year construction period, how quickly was the height increasing when the pyramid was 75 metres tall? State your answer in metres per year. 5. (20 points) Recall 180 & = & is the conversion from degrees to radian. Use linear approximation to estimate sin 35 & . Hint: You know sin 30 & already, & will feature in your expression. 2...
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04_Midterm2-Sample - t 2 feet(a(6 points What is the...

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