MIT OpenCourseWare http://ocw.mit.edu 18.01 Single Variable Calculus For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Fall 200618.01 Exam 2Tuesday, Oct. 17, 2006Problem 1. (15 pts.) Estimate the following to two decimal places (show work) a. (8 pts.) sin( 1/100)π+b. (7 pts.) 101Problem 2. (20 pts.) Sketch the graph of 41yxx=++onx−∞< <∞and label all critical points and infection points with their coordinates on the graph along with the letter “C” or “I”Problem 3. (20 pts.) An architect plans to build a triangular enclosure with a fenceon two sides and a wall on the third side. Each of the fence segments has fixed Length L. What is the length x of the third side if the region enclosed has the largest possible area? Show work and include an argument to show that your answer reallygives the maximum area. Problem4. (15 pts) A rocket has launched straight up, and its altitude is h = 10t2feet after t seconds. You are on the ground 1000 feet from the launch site. The lineof sight from you to the rocket makes an angle θ with the horizontal. By how manyRadians per second is θ changing ten seconds after the launch? Write down on which intervals the function is: Increasing: Decreasing: Concave down:Problem 5. a. (10 pts) Evaluate the following indefinite integrals i.∫cos(3x)dx∫xe()x2ii.dxb. (10 pts) Findy()xsuch that y11=y3andy(0)=1Problem 6. (10 pts.) Suppose that f '(xe) =()x2, and f (0)=10One can conclude from the mean value theorem thatAf< (1) < Bfor which numbers A and
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