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Unformatted text preview: Sample Math 115 Final Exam Fall Semester 2011 • The midterm examination is on Thursday, December 15 at 4:30PM  7:00PM . • Room assignments are the same as for the common midterm exam and will be an nounced in classes and posted outside the math office (405 Snow). • Only simple graphing calculators (TI84 plus and below) are allowed for the common exams. You will mark your answers on both exam booklets and provided bubble sheets . You are considered responsible to bring pens/pencils and a calculator to the common exams. Pens or pencils will not be provided for you, and interchanging calculators will be prohibited during the exams. • The common final exam covers – Chapter 2: Sections 2.1, 2.2, 2.3, 2.4, 2.5, 2.6; – Chapter 3: Sections 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7; – Chapter 4: Sections 4.1, 4.2, 4.3, 4.4, 4.5; – Chapter 5: Sections 5.1, 5.2, 5.4, 5.5, 5.6; – Chapter 6: Sections 6.1, 6.2, 6.3, 6.4, 6.5 • The problems below, all multiplechoice with exactly one correct answer, are intended to be reasonably representative of what might appear on the actual exam, which will have 30 problems. 1 1. Let f ( x ) = x x 2 +1 and g ( x ) = 1 x . Then, ( g ◦ f )( x ) is (A) x x 2 + 1 (B) 1 x (C) x + 1 x (D) x (E) None of the above 2. Suppose that F ( x ) = f ( x ) 2 + 1, f(1) = 1, and f (1) = 3. Find F (1). (A) 3 (B) 4 (C) 5 (D) 6 (E) None of the above 3. The unit price p and the quantity x demanded are related by the demand equation 50 p ( x 2 + 1) = 0. Find the revenue function R = R ( x ). (A) 50 x x 2 + 1 (B) 50 x 2 + 1 (C) x x 2 + 1 (D) x 2 + 1 50 (E) None of the above 4. Find the marginal revenue for the revenue function found in Problem 3. (A) 100 x ( x 2 + 1) 2 (B) 1 x 2 ( x 2 + 1) 2 (C) x 25 (D) 50(1 x 2 ) ( x 2 + 1) 2 (E) None of the above 5. Find dy dx in terms of x and y when x and y are related by the equation x 1 / 3 + y 1 / 3 = 1. (A) x y ! 2 / 3 (B) y x 2 / 3 (C) x y ! 1 / 3 (D) y x 1 / 3 (E) None of the above 6. Find dy dx at point (2 , 2 √ 5) when x and y are related by the equation y 2 x 2 = 16. (A) √ 5 5 (B) √ 5 (C) 5 √ 5 (D) 1 5 √ 5 (E) None of the above 7. Let f ( x ) = √ x +1 x 2 . The domain of f is (A) (∞ , 2) and (2 , + ∞ ) (B) (∞ , 2] and [2 , + ∞ ) (C) [ 1 , 2) and (2 , + ∞ ) (D) [ 1 , + ∞ ) (E) None of the above 8. Let f ( x ) = ln(2 x ). The domain of f is (A) (∞ , + ∞ ) (B) (0 , + ∞ ) (C) (∞ , 0) (D) (∞ , 2) (E) None of the above 2 9. Evaluate: lim x → 3 (3 x 2 4). (A) 23 (B) 5 (C) 4 (D) The limit does not exist (E) None of the above 10. Evaluate lim x → 5 x 2 2 x 15 x 5 ....
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This note was uploaded on 03/15/2012 for the course MATH 115 taught by Professor Bayer,margaret during the Fall '08 term at Kansas.
 Fall '08
 Bayer,Margaret
 Math, Calculus

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