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

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1 MA3 Elem. Calculus Fall 07 Exam Name: Sec.: Do not remove this answer age you will turn in the entire exam. No books or notes may be used. You may use an ACT-aroved calculator during the exam, but NO calculator with a Comuter Algebra System (CAS), networking, or camera is ermitted. Absolutely no cell hone use during the exam is allowed. The exam consists of two short answer questions and twenty multile choice questions. Answer the short answer questions on the back of this age, and record your answers to the multile choice questions on this age. For each multile choice question, you will need to ll in the circle corresonding to the correct answer. It is your resonsibility to make it CLEAR which resonse has been chosen. For examle, if (a) is correct, you must write a b c d e You have two hours to do this exam. Please write your name and section number on this age. 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. a b c d e 4. a b c d e 6. a b c d e. 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: Multile Choice Short Answer Total (number right) ( oints each) (out of 0 oints) (out of 00 oints)

2 Fall 07 Exam Short Answer Questions Write answers on this age. Your work must be clear and legible to be sure you will get full credit.. Find the derivative of h x final answer. e 4x 3 9ln x. Do NOT simlify your answer. Clearly circle your. Boyle s Law states that when a samle gas is comressed at a constant temerature, the ressure P and the volume V satisfy the equation PV c, where c is a constant. Suose that at a certain instant the volume is 700 cm 3, the ressure is 300 kpa, and the volume is increasing at a rate of 4 cm 3 er minute. At what rate is the ressure decreasing at this instant? (Show stes clearly and circle your final answer.)

3 Name: Multile Choice Questions Show all your work on the age where the question aears. Clearly mark your answer on the cover age on this exam. 3. For the function f(x) = 7x 3 + 8x + x + 9, nd the equation of the tangent line to the grah of f at x =. (a) y = 07x 93 (b) y = 07 (c) y = x 3 (d) y = x + 07 (e) y = x Find the derivative, f 0 (x), if f(x) = 6x 3 + 7x + 8x + 4. (a) (=)(6x 3 + 7x + 8x + 4)(8x + 4x + 8) (b) 8x + 4x + 8 (c) (=)(6x 3 + 7x + 8x + 4) = (d) (=)(6x 3 + 7x + 8x + 4) 4= (8x + 4x + 8) 8x + 4x + 8 (e) 6x3 + 7x + 8x + 4. Find the derivative, f 0 (x), if f(x) = (80x + 70) ln(9x + ). (a) x+ (b) (80x + 70) + 80 ln(9x + ) 9x+ (c) 80 ln(9x + ) (d) 9e 9x (e) (80x + 70) ln(9x + ) 9x+ 3

4 6. Suose F (x) = (x + 6)e g(x). If g(9) = 0; and g 0 (9) = 8, nd F 0 (9). (a) 0 (b) 6 (c) (d) 0 (e) 8 7. Suose g(7) = 6 and g 0 (7) =. Find F 0 (7) if F (x) = x g(x) (a) (b) (c) (d) 6 36 (e) Suose H(x) = f(x) + g(x). If f(8) = 4, f 0 (8) = 7, g(8) = 4, and g 0 (8) = 6, nd H 0 (8). (a) 4 (b) 6 (c) 3 (d) 637 (e)

5 9. Suose F (x) = ln(g(x)). If g() =, g 0 () = 7, and g 00 () =, then nd F 0 (). (a) ln () =7 (b) 7= (c) =7 (d) = ln (7) (e) ln () 0. For the function f(x) = at x = 6. (a) (b) 40 (c) 4088 (d) 47 (e) 3 8 >< >: x 9 x < 0 x x < 0, nd the sloe of the tangent line to the grah of f x x. Find the derivative, f 0 (x), if f(x) = e 9+x. 0 C A 9 + x (a) e (b) 9 + x 9 + x (c) (d) 9 + x e 9+x 9 + x e x (e) ln( 9 + x)

6 . If f(x) = x 8 + 7x + 8x then nd the third derivative f 000 (x): (a) 67x + 7x (b) 6x7 + 4x + 8 x (c) 04x 8 + 6x (d) 67x (e) x If f(x) = (4x + 36) 7 then f 00 (x) = (a) 7(6) (4x + 36) (4) (b) 0 (c) 7 (4x + 36) 6 (d) 7 (4) 7 (4x + 36) (e) 7(6)4 4. Find the derivative, f 0 (x), of f(x) = x 60 (a) =(60 x 9 ) (b) 60x 9 (c) 60x 6 (d) 60x 9 (e) =(60 x 6 ) 6

7 . If an amount of x dollars is invested at % interest comounded continuously, and at the end of years the value of the investment is $6000, nd x. (a) $43.6 (b) $.87 (c) $36.7 (d) $49.0 (e) $ The number of bacteria in a culture doubles every 7 hours. If we begin with 000 cells, about how many cells do we have after 0 hours? (a) 6 cells (b) 87 cells (c) 6,807,000 cells (d) 4804 cells (e) 69 cells 7

8 7. A circle is growing so its area is increasing at a rate of 9 square feet er minute. At what rate is the radius changing when its radius is feet? (a) 90 feet er minute (b) (c) 0 9 (d) (e) 9 feet er minute feet er minute feet er minute feet er minute 8. It is estimated that the annual advertising revenue received by a certain newsaer will be R(x) = 0:x + 9x + 9 thousand dollars when its circulation is x thousand. The circulation of the aer is currently 7000 and is increasing at a rate of 000 aers er year. At what rate will the annual advertising revenue be increasing with resect to time 3 years from now? (a) $000:00 er year (b) $64000:00 er year (c) $49:0 er year (d) $00:00 er year (e) $4900:00 er year 8

9 9. The grah of y = f(x) is shown below. The minimum value of f(x) on the interval [ 3; 4] occurs at which x? (a) 3 (b) (c) 4 3 y (d) (e) x Find the minimum value of g(t) = t 3 48t + 70 on the interval [ ; ]. (a) 4 (b) 98 (c) 8 (d) 8 (e) 36 9

10 Some Formulas. Areas: (a) Triangle A = bh (b) Circle A = r (c) Rectangle A = lw (d) Traezoid A = h + h. Volumes: b (a) Rectangular Solid V = lwh (b) Shere (c) Cylinder V = 4 3 r3 V = r h (d) Cone V = 3 r h 0

11 MA3 Elem. Calculus Fall 07 Exam Name: Sec.: Do not remove this answer age you will turn in the entire exam. No books or notes may be used. You may use an ACT-aroved calculator during the exam, but NO calculator with a Comuter Algebra System (CAS), networking, or camera is ermitted. Absolutely no cell hone use during the exam is allowed. The exam consists of two short answer questions and twenty multile choice questions. Answer the short answer questions on the back of this age, and record your answers to the multile choice questions on this age. For each multile choice question, you will need to ll in the circle corresonding to the correct answer. It is your resonsibility to make it CLEAR which resonse has been chosen. For examle, if (a) is correct, you must write a b c d e You have two hours to do this exam. Please write your name and section number on this age. 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. a b c d e 4. a b c d e 6. a b c d e. 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: Multile Choice Short Answer Total (number right) ( oints each) (out of 0 oints) (out of 00 oints)