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1 MA Elem. Calculus Fall 07 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 twenty 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 and section number on this page. GOOD LUCK!. a b c d e. a b c d e 4. a b c d e. 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 Fall 07 Exam Short Answer Questions Write answers on this page. You must show appropriate clear steps to be sure you will get full credit.. Evaluate the limit: x lim x 5 x 4x 5 6x 5 Final answer:. Let f x x x 0. Find the equation of the tangent line to f x at x. Equation of tangent line:
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.. The expression can be simplied to which of the following? x 4 (x) 6 x 8 (a) x (b) 64x 4 (c) 64x (d) x 4 (e) x 8 4. Find the domain of the function f(x) = p 6 x: (a) [0; ] (b) ( ; 6] (c) [6; ) (d) ( ; 6) (e) (6; )
4 5. If h(t) represents the height of an object in feet above ground level at time t seconds and h(t) is given by h(t) = 6t + t + 8, nd the time at which the speed of the object is zero. (a) 8 seconds (b) (5=) seconds (c) (=6) seconds (d) (69=6) seconds (e) (=) seconds 6. If f(x) = p x + 4 then choose the simplied form of (a) p x + h p x + 4 (b) p x + h + 4 (c) p (d) x + h + 4 p x + 4 f (x+h) f (x) h : px (e) h p x + 4 4
5 7. The graph of y = f(x) is shown below. Compute the average rate of change of f(x) from x = to x =. (a) 5 (b) 5 (c) (d) (e) 5 4 y x 8. Let f(x) = x. Find a value c between x = 0 and x = 8, so that the average rate of change of f(x) from x = 0 to x = 8 is equal to the instantaneous rate of change of f(x) at x = c. You may use the fact that f 0 (x) = x. (a) 9 8 (b) p (c) 6 8 (d) p 5 (e) p 8 5
6 9. If lim f(x) = and lim g(x) = 7, then what is the value of lim x! x! x! (a) 7 (b) 0 (c) the limit is innity or does not exist (d) ( + 5)( + ) 7 (e) ()() 7 (x + 5)(f(x) + )? g(x) 0. Find the limit x 6 lim x!6 x 6 (a) 0 (b) 6 6 (c) 40 (d) (e) This limit either tends to innity or this limit fails to exist 6
7 . Find the limit 6 p t lim t! t (a) 8 (b) p 8 t (c) 6 (d) 0 (e) This limit either tends to innity or this limit fails to exist. Find the limit lim n! (4n + ) n 5 + 4n + (a) 0 (b) 4 (c) The limit does not exist or approaches innity (d) 6 (e) 6 7
8 . For the function nd lim x!5 + f(x) f(x) = 8 >< >: j4 + 8xj if x < p x + 6 if x < x + x + 5 if x (a) p (b) 85 (c) p 5 (d) 5 (e) The graph of y = f(x) is shown below. Compute lim f(x). x! (a) The limit does not exist or approaches innity (b) 0 (c) (d) (e) y x
9 5. Consider the function f(x) = ( x 4 if x < 8 x + B if x 8 Find a value of B so that the function is continuous at x = 8. (a) 4 (b) 4 (c) 4 (d) 44 (e) Find all values of x where the derivative is not dened for f(x) = jx 4x + 45j: (a) x = 5 and x = 9 (b) x = -4 and x = 45 (c) x = -4 only (d) x = 45 only (e) x = 0 and x = 45 9
10 7. Suppose that for a function f(x), we know that f(x + h) h f(x) = xh h 8h h(x + 8) (x + h + 8) : Find the slope of the tangent line at x = 7. (a) (b) 4 5 (c) 5 4 (d) 0 (e) The slope does not exist. 8. Consider the function f(x) = x + 4x + 7. Its tangent line at x = goes through the point (6; y ) where y is: (a) 0 (b) 58 (c) 6 (d) (e) 8 0
11 9. Determine the value of f 0 () from the graph of f(x) given here: y (a) f 0 () = 0 (b) f 0 () = (c) f 0 () = (d) f 0 () = (e) f 0 () = x The graph of y = f(x) is shown below. The function is continuous, except at x = (a) x=, x=, and x=4 (b) x= and x=4 (c) x= only (d) x=4 only (e) x=, x=, x=4, and x=6 5 4 y - x
12 MA Elem. Calculus Fall 07 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 twenty 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 and section number on this page. GOOD LUCK!. a b c d e. a b c d e 4. a b c d e. 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)
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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