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Unformatted text preview: MATH 191, Sections 1 and 3 Calculus I Fall 2007 Practice Exam 2 This practice exam, like the actual exam will be, is worth a total of 100 points, and point values for each question are given below. It is similar in length, format, and tested content to the actual exam, but in the interest in saving paper I have omitted space for you to work your solutions; you should work these out on your own paper. Answer every question fully and clearly. Please show your work where appropriate, and circle or box your final answer. Please let me know if you have any questions! 1. (24 points total, 8 points each) Suppose we know that f (1) = 3, f (1) = 2, g (1) = 1, and g (1) = 4. (a) Find ( f g ) (1). We need the Quotient Rule, of course: ( f g ) (1) = f (1) g (1) g (1) f (1) ( g (1) ) 2 = 2 · 1 4 · 3 1 2 = 14 . (b) Find ( fg ) (1). Here, it’s the Product Rule: ( fg ) (1) = f (1) g (1) + f (1) g (1) = 2 · 1 + 4 · 3 = 10 . (c) Find ( f ◦ g ) (1). Here, finally, it’s the Chain Rule: ( f ◦ g ) (1) = f ( g (1)) · g (1) = f (1) · g (1) = 2 · 4 = 8 . 2. (20 points) While breakfasting one morning in the Caf, you come across a small lump of metallic material in your oatmeal. Intrigued, you take it to the physics lab and test it with a geiger counter, which goes wild when you sweep it over the lump. It’s radioactive! But what is it? After determining its mass to be precisely 100 grams, a hardness test narrows it down to either cobalt or iron. Just as you feel you’re about to pin down the lump’s identity once and for all, youcobalt or iron....
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 Fall '07
 BAHLS
 Calculus, Chain Rule, Derivative, dy dy dy

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