a b c d e GOOD LUCK! 3. a b c d e 12. a b c d e 4. a b c d e 13. a b c d e 5. a b c d e 14. a b c d e 6. a b c d e 15. a b c d e

Transcription

1 MA3 Elem. Calculus Spring 06 Exam Name: Sec.: Do not remove this answer page you will turn in the entire exam. No books or notes may be used. You may use an ACT-approved calculator during the exam, but NO calculator with a Computer Algebra System (CAS), networking, or camera is permitted. Absolutely no cell phone use during the exam is allowed. The exam consists of two short answer questions and eighteen multiple choice questions. Answer the short answer questions on the back of this page, and record your answers to the multiple choice questions on this page. For each multiple choice question, you will need to ll in the circle corresponding to the correct answer. It is your responsibility to make it CLEAR which response has been chosen. For example, if (a) is correct, you must write a b c d e You have two hours to do this exam. Please write your name on this page, and at the top of page three. GOOD LUCK! 3. a b c d e. a b c d e 4. a b c d e 3. a b c d e 5. a b c d e 4. a b c d e 6. a b c d e 5. a b c d e 7. a b c d e 6. a b c d e 8. a b c d e 7. a b c d e 9. a b c d e 8. a b c d e 0. a b c d e 9. a b c d e. a b c d e 0. a b c d e For grading use: Multiple Choice Short Answer Total (number right) (5 points each) (out of 0 points) (out of 00 points)

2 Spring 06 Exam Short Answer Questions Write answers on this page. You must show appropriate legible work to be sure you will get full credit. 4 pts. Evaluate the one-sided limit x lim x 0 6 x. 6 pts f x x 3. Find a value of x. Let such that the average rate of change of f x from to x equals.

3 Name: Multiple Choice Questions Show all your work on the page where the question appears. Clearly mark your answer both on the cover page on this exam and in the corresponding questions that follow. 3. Solve the equation t = r + k 5 w for w (a) w = 5r 5t k (b) w = 5t k 5r (c) w = (d) w = 5t r + k t r + k 5 (e) w = 5t k 5r 4. Evaluate f(4) when f(x) is given by the piecewise denition f(x) = 8 >< >: x 7 if x 3 x if 3 < x 4 x 5x if 4 < x (a) 4 (b) 7 (c) (d) 9 (e) DNE 3

4 5. A train travels from city A to city B, then travels from city B to city C. The train leaves city A at 9:00am and arrives at city B at :00am. The train leaves city B at :00am and arrives at city C at 4:00pm. The average velocity of the train, while traveling from A to B, was 3 miles per hour. What was the average velocity of the train from city B to city C, given that the average velocity of the train while traveling from A to C was 54 miles per hour? (a) (85=) miles per hour (b) (36=5) miles per hour (c) (3=5) miles per hour (d) (3=) miles per hour (e) 85 miles per hour 6. If f(x) = p x + 3 then choose the simplied form of p p (a) x + h + 3 x + 3 (b) (c) p x + h + 3 f (x+h) f (x) h : (d) hp x p x + 3 (e) p x + h p x + 3 4

5 7. Let f(x) = 3x + 4. Find a value of x so that f 0 (x) = 36. (a) x = (b) x = 3 (c) x = 4 (d) x = 5 (e) x = 6 8. Let f(x) = 6x + 4x + 3. Find a value c between x = 3 and x = 7, so that the average rate of change of f(x) from x = 3 to x = 7 is equal to the instantaneous rate of change of f(x) at x = c. (a) 3 (b) 4 (c) 5 (d) 6 (e) 7 5

6 7f(x) + 9. If lim f(x) = and lim g(x) = 7, then what is the value of lim x!3 x!3 x!3 x + g(x)? (a) 0 (b) (7) (c) the limit is innity or does not exist (d) (7)()(3) (7)(3) (e) 7 0. Find the limit x 6 lim x!34 x 34 (a) 6 34 (b) 38 (c) 0 (d) (e) This limit either tends to innity or this limit fails to exist 6

7 . Find the limit 5 lim x!0 x 5x 5 + x (a) This limit does not exist. (b) 5 (c) 0 (d) 5 (e). Find the limit lim n! (n + 3) 3n + (a) 3 (b) The limit does not exist or approaches innity (c) (d) (e)

8 3. For the function nd lim x!3+ f(x) f(x) = 8 >< >: j3 + 4xj if x < p x + 4 if x < 9x + 4x + 8 if x (a) p 3 (b) p 8 (c) 5 (d) 5 (e) 0 4. The graph of y = f(x) is shown below. Compute lim x! f(x). (a) 5 (b) (c) The limit does not exist or approaches innity (d) 3 (e) y x

9 5. Consider the function f(x) = ( x 3 if x < 4 x + B if x 4 Find a value of B so that the function is continuous at x = 4. (a) (b) 3 (c) 4 (d) 5 (e) 6 6. Find the value of m which makes f(x) dierentiable everywhere, where ( x ; if x 3; f(x) = m ( 3 + x) + 9; if x > 3 (a) 6 (b) 7 (c) 8 (d) 9 (e) 0 9

10 7. Find the equation of the tangent line to the graph of the function f(x) = + 3 at x = 3. You x + may use f 0 x (x) = (x + ) (a) y = 3 0 (b) y = 3 0 x 34 5 (c) y = x (d) y = (e) y = 3 50 x x Consider the function f(x) = 6x + 4x + 5. Its tangent line at x = 4 goes through the point (8; y ) where y is: (a) 7 (b) 00 (c) 35 (d) 5 (e) 9 0

11 9. The graph of y = f(x) is shown below. f 0 ( ) is approximately : (a) (b) (c) The limit does not exist or tends to innity (d) (e) y - x The graph of y = f(x) is shown below. The function is dierentiable, except at x = (a) x=4 only (b) x= and x=4 (c) x=, x=3, and x=4 (d) x= only (e) x=, x=3, x=4, and x= y - x

12 MA3 Elem. Calculus Spring 06 Exam Name: Sec.: Do not remove this answer page you will turn in the entire exam. No books or notes may be used. You may use an ACT-approved calculator during the exam, but NO calculator with a Computer Algebra System (CAS), networking, or camera is permitted. Absolutely no cell phone use during the exam is allowed. The exam consists of two short answer questions and eighteen multiple choice questions. Answer the short answer questions on the back of this page, and record your answers to the multiple choice questions on this page. For each multiple choice question, you will need to ll in the circle corresponding to the correct answer. It is your responsibility to make it CLEAR which response has been chosen. For example, if (a) is correct, you must write a b c d e You have two hours to do this exam. Please write your name on this page, and at the top of page three. GOOD LUCK! 3. a b c d e. a b c d e 4. a b c d e 3. a b c d e 5. a b c d e 4. a b c d e 6. a b c d e 5. a b c d e 7. a b c d e 6. a b c d e 8. a b c d e 7. a b c d e 9. a b c d e 8. a b c d e 0. a b c d e 9. a b c d e. a b c d e 0. a b c d e For grading use: Multiple Choice Short Answer Total (number right) (5 points each) (out of 0 points) (out of 00 points)