PracticeProbPrelim

PracticeProbPrelim - Calculus 135 Practice Problems Set 1...

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Practice Problems Set 1 This are introductory problems. These problems, for the most part, should be a review of skills learned in high school algebra. 1. Calculation Review. a. Solve for x if x 3 - x 5 = 4 b. Let s = at a + t . Solve for t in terms of a and s . c. Evaluate 4 x 0 + x 2 3 + x - 2 3 when x = 27. d. Suppose that y = 3 x . Express 3 x - 2 in terms of y . 2. Word Problems and Functions. a. The area of a rectangle is 204 square feet. The perimeter of the rectangle is 58 feet. Find the dimensions of the rectangle. b. A ladder 10 feet tall is standing vertically against the side of a barn so that it is perpendicular to the ground. Elmo moves the foot of the ladder along the ground so that the foot of the ladder is 6 feet away from the barn. How many feet did the top of the ladder slide down the barn. c. A rectangular box has no top, and a volume of 2 . 4 cubic meters. The length l is three times the width. Let w be the width of the rectangular base and let h be the beight of the box. i. Make a sketch of the box, with the dimensions labeled. ii. Give a formula for h as a function of w . What is the domain of h ? iii. Can you give a formula for w as a function of h ? Why or why not? iv. Give a formula for the surface area S of the box as a function of w . d. An open box is to be made by cutting squares of length x from the four corners of a sheet of cardboard which is 24 inches wide and 32 inches long and then turning up the sides. Give an expression for the volume V of the box as a function of
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PracticeProbPrelim - Calculus 135 Practice Problems Set 1...

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