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101-2004&amp;2005-1-M20-December2004

# 101-2004&amp;2005-1-M20-December2004 - i'wait...

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i'wait University Math 101 Date: December 16, 2004 pt. of Math. & COIUp. Sci. Second Exam Duration: 75 minutes Calculators, mobile phones, pagers and all other mobile communication equipment are not allowed Answer the following questions: J () )3 + x .. VI9 1. Let x = ---. Use differentIals to approXImate --. x 0.9 2. Find equations of the normal lines to the graph of the equation 4x + y2 + (xy) 2 = 6 at the point whose x-coordinate is 1. (3 pts.) (4 pts.) (10 pts.) 3. (a) State The Mean Value Theorem. I..=:, @Suppose that J is continuous on [a, u] and l' (x) < 0 for every x E (a, b). Use The . ( Mean Value Theorem to show that J (b) < J (a). (4 pts.) 4. Two students start walking from the same point. One walks south at a rate of 4 rn/sec and the other walks west' at a rate of 3 m/sec. At what rate is the distance between the two students increasi~g 2 seconds later. (4 pts.) x 5. Let J (x) = x + 1. (a) Find the vertical and horizontal asymptotes for the graph of J, if any. 1 fb) Show that l' (x) =')' Find the intervals on which the graph of J is in- (x + It creasing and the intervals on which the graph of J is decreasing.

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101-2004&amp;2005-1-M20-December2004 - i'wait...

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