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Midterm1ReviewSolutions - Math 016 Review sheet for Midterm...

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Unformatted text preview: Math 016 Review sheet for Midterm I Tuesday, March 11, 2008, 8-10PM 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.

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Midterm1ReviewSolutions - Math 016 Review sheet for Midterm...

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