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Unformatted text preview: The Return of More Problems
(1) Differentiate the following functions. (a) (c) (e) y = ln(arcsin(3x) + 1) y = x arccos
2 (b) y = sin(arctan(ln x + x)) arctan(e x ) (d) y = 1 + x2 ex x2 y = arcsin xearctan x (2) A rectangle is to have fixed perimeter P . What dimensions give maximal area? (3) An isosceles triangle has base and height h. Find the maximum area of an inscribed rectangle with one side on the base of the triangle. (4) At which points on the curve y = 1 + 40x3 - 3x5 does the tangent line have the largest slope? (5) A person walks down straight path at 6 ft/sec. She is followed by a spotlight, whose minimum distance to the path is 30 ft. How fast is the spotlight turning when the person is 50 ft from the point where the spotlight is closest to the path? (6) A right circular cylinder is inscribed inside a cone with base radius R and height H. Find the largest possible volume of the cylinder. ...
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This homework help was uploaded on 04/09/2008 for the course M 408c taught by Professor Mcadam during the Fall '06 term at University of Texas at Austin.
- Fall '06