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Unformatted text preview: Math 016 Review sheet for Midterm I Tuesday, March 11, 2008, 810PM at C20 PC. You need # 2 pencil and a picture ID (covers material up to (and including) section 3.5) The exam will be in the form of multiple choices as most of the university’s large classes. 1. Given f ( x ) = 2 x 3 5 x + 4, then f ( 1) is: (a) 1 (b) 11, (c) 7, (d)3, (e) None of the above. Solution: f ( 1) = 2( 1) 3 5( 1) + 4 = 2 + 5 + 4 = 7. 2. The equation of the line joining the points (1, 1) and (3, 3). (a) y = 3 x + 2.(b) y = 2 x 3, (c) y = x 1, (d) x + y = 4, (e) None of the above. Solution: y y = m ( x x ) y + 1 = 3 + 1 3 1 ( x 1) y = 4 2 ( x 1) 1 y = 2 x 3 3. Given f ( x ) = x 2 and g ( x ) = √ x 1, find: ( f ◦ g )(5) is (a) 1, (b) 2, (c) 3, (d)4, (e) None of the above. Solution: ( f ◦ g )(5) = f ( g (5)) = f ( √ 5 1) = f (2) = 2 2 = 4. 4. The average rate of change of g ( x ) = 1 x , x = 2 , Δ x = 0 . 1 (a) 5/21, (b)1/2, (c)5/21, (d).1, (e) None of the above. g (2 + Δ x ) g (2) Δ x = g (2 . 1) g (2) . 1 = 1 2 . 1 1 2 . 1 = 2 2 . 1 4 . 2 . 1 = . 1 4 . 2 . 1 = . 1 . 1(4 . 2) = 1 4 . 2 = 5 21 5. The average rate of change of f ( x ) = x 2 , at x = 1 with Δ x = 0 . 1 is (a) 1, (b)2.1, (c) 21, (d)1.21, (e) None of the above. f (1 + Δ x ) f (1) Δ x = f (1 . 1) f (1) . 1 = (1 . 1) 2 1 2 . 1 = 1 . 21 1 . 1 = 2 . 1 6. The limit of lim x → 2 x 2 + 1 x + 2 (a)5/4, (b)3/4, (c)1, (d) Does not exist, (e) None of the above. Answer: a. The function is continuous at x = 2 so the limit is (2 2 + 1) / (2 + 2) = 5 / 4. 7. The limit of lim x → 2 x 2 x 2 x 2 (a) 3, (b)3, (c)0, (d) Does not exist. (e) None of the above. Answer: b. 3 lim x → 2 x 2 x 2 x 2 = lim x → 2 ( x 2)( x + 1) x 2 = lim x → 2 ( x + 1) = 2 + 1 = 3 8. The limit of lim x → 2 x 2 + x 2 x + 2 (a) 3, (b)0, (c)3, (d) Does not exist. (e) None of the above. Answer: c. lim x → 2 x 2 + x 2 x + 2 = lim x → 2 ( x + 2)( x 1) x + 2 = lim x → 2 ( x 1) = 2 1 = 3 9. The limit of lim x → 1 x 2 x 2 x 2 (a)0, (b)2, (c)2, (d)Does not exist. (e) None of the above. Answer: b. The function is continuous at x = 1 so the limit is (1 2 1 2) / (1 2) = 2 / 1 = 2....
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This note was uploaded on 03/27/2008 for the course MATH 016 taught by Professor Victorcamillo during the Spring '08 term at University of Iowa.
 Spring '08
 VictorCamillo
 Math, Calculus, Logic

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