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quiz7-10.40-soln.

# quiz7-10.40-soln. - MATH 101-B Fall 2004 Quiz 7(10:40-12:30...

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Unformatted text preview: MATH 101-B Fall 2004 Quiz 7 (10:40-12:30 Group) November 26, 2004 Time: 10 minutes Name: Student No: Follow the directions. No work Problem 1 (4 pts.) If f x Solution. cos arcsin x 2 No credit!! 1 sin arcsin x 2 1 sin arcsin x 2 fx 1 2x x 2 1 arcsin x 2 1 1 1 x2 1 2 1 x2 , find f x . Simplify the derivative. 1 2 Problem 2 (6 pts.) Given the curve x 3 sin y x y Write the equation of the tangent line to this curve at the point 0, 0 . Solution. Taking d dx of both sides (implicit differentiation) yields dy dy 3x 2 cos y 1 dx dx dy 3x 2 1 cos y 1 0 dx Substituting x, y 0, 0 in this equation yields dy 1 2 0 dx dy 1 2 dx Hence, the slope of the tangent line at 0, 0 is 1/2 and its equation is 1x 0 y0 2 1x y 2 2x ...
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