Math.111HW4(2008-2009,Fall)

# Math.111HW4(2008-2009,Fall) - Due on Nov.26 for 04 05 07...

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“Due on Nov.26 for sections 01, 02, 04, 05, 07. Due on Nov.27 for sections 03, 06. Bring the homework to the first lecture on the due date. Homework 4 1. Two parallel sides of a rectangle are being lengthened at the rate of 3 in/sec, while the other two sides are shortened in such a way that the figure remains a rectangle with constant area 60 in 2 . (i) What is the rate of change of the perimeter of the rectangle when the length of an increasing side is 6 in? (ii) What are the lengths of the sides of the rectangle when the perimeter stops to decrease? 2. (a) Write the equations of the tangents and the normals lines to the curve x 3 = y 2 - 2 y at the point(s) where the curve crosses the y -axis. (b) The curves x 2 = 4 y and 2 y 2 = 12 - 5 x intersect at the points (2 , 1) and ( - 4 , 4) . Find the (acute) angles between the curves at the intersection points. 3. (a) Using an appropriate linearization of the function x at a point, find 4 . 1 approximately.

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