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quiz7-8.40-soln.

quiz7-8.40-soln. - MATH 101-B Fall 2004 Quiz 7(8:40-10:30...

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Unformatted text preview: MATH 101-B Fall 2004 Quiz 7 (8:40-10:30 Group) November 26, 2004 Time: 10 minutes Name: Student No: Follow the directions. No work Problem 1 (4 pts.) If f x arctan ln 3x 2 No credit!! 7 , find f x . Solution. fx 1 1 Problem 2 (6 pts.) Given the curve x 3 to this curve at the point 1, 2 . Solution. Taking d dx 1 l n 3x 2 1 l n 3x 2 y 7 2 7 2 xy 2 l n 3x 2 6x 3x 2 7 7 1. Write the equation of the tangent line of both sides (implicit differentiation) yields dy dy 3x 2 y 2 x 2y 0 dx dx dy 3x 2 y 2 1 2xy 0 dx Substituting x, y 1, 2 in this equation yields dy 34 14 0 dx dy 1 3 dx Hence, the slope of the tangent line at 1, 2 is 1/3 and its equation is 1x 1 y2 3 1x 7 y 3 3 ...
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