SFU Math 100 Midterm 1 - October 4, 2006, Exams of Calculus

Download SFU Math 100 Midterm 1 - October 4, 2006 and more Exams Calculus in PDF only on Docsity! 1 Simon Fraser University Math 100 Midterm 1 Date: October 4, 2006 Time: 11:30 - 12:20am Last Name (print): First Name Signature: SFU Email ID: Instructor: Laura Chávez Lomeĺı. Instructions: 1. Do not open this exam until instructed to do so. 2. No calculators, notes or books are allowed. 3. When presenting a final answer for your solution, calculator-ready expressions will be given full credit. 4. Show all your work. No credit will be given for an answer without the correct accompanying work. 5. Answer the questions in the space provided. Continue on the back of the previous page if necessary. Question Mark Maximum 1 10 2 8 3 4 4 9 5 9 Total 40 2 1. Given the function: f(x) = −(x − 4)2 + 4 defined for 0 < x ≤ 8: (a) Draw the graph of f(x).[6 marks] 0 60 120 180 240 0 60 120 180 240 (b) Is the function one to one? Explain.[2 marks] (c) Determine the range of f(x).[2 marks] 5 4. Let f(x) = x2 − 4 and g(x) = 3x2 + 12x + 12 (a) Find g(f(x)).[3 marks] (b) Find h(x) = f(x) g(x) and simplify as much as possible.[4 marks] (c) Determine the domain of h(x).[2 marks] 6 5. Consider the points P = (−3, 1), Q = (5, 15) and R = (0,−3). (a) Find the midpoint of the segment with endpoints P and Q.[2 marks] (b) Calculate the distance between P and R.[2 marks] (c) Determine the equation of the circle with center Q and radius equal to the distance[2 marks] between P and R (as found in part 5b). (d) What is the standard form of the equation of the circle: x2 + y2 + 6x − 8y + 8 = 0?[3 marks]