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Unformatted text preview: Midterm Examination Math 1A Professor J. Harrison November 13, 2009 WRITE YOUR NAME and GSI ON EACH PAGE. Show your work and justify statements. Calculators are not permitted. Turn your exam into your GSI and show your ID card. If you need more space to answer a question, you may continue your answer on the back of the page with the question on it. Name: SID: GSI: Section: (1) (2 pts) Calculate lim x + x x . Since exp ( x ) = e x is a continuous function and exp ln ( x ) = x , we have lim x + x x = lim x + exp ln ( x x ) = lim x + exp ( xlnx ) = exp lim x + lnx 1 x . By LHopitals Rule, lim x + lnx 1 x = lim x + 1 x- 1 x 2 = lim x + (- x ) = 0. Therefore, lim x + x x = exp (0) = 1. (2) (2 pts) A hot air balloon is ascending at the rate of 12 ft/sec and is at a height of 80 ft above the ground when a donut is dropped into a crowd of students in Sproul plaza. How long goes it take the donut to reach the ground, assuming no one catches it first? (Acceleration due to the gravitational force near the surface of the earth is 32 ft/sec...
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- Fall '08