MATH 124 Midterm: MATH 124 UW 124 Winter 12 Sol2
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MATH 124 Full Course Notes
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Math 124, section g, winter 2012, solutions to midterm ii: find dy dx for the following functions. Check your answers. (a) (2 points) y = 7 + ln x y = 2x 7 + ln x (b) (4 points) 3x2y3 + 5xy sin y + ex = 9. Y cos y + ex = 0 so (c) (4 points) y = x(x+cos2 x) Take ln of both sides: di erentiate both sides y = 6xy2. 9x2y2 + 5x cos y ln y = (x + cos2 x) ln x y y. 1 x solve for y y = (cid:18)(1 2 cos x sin x) ln x + x + cos2 x x (cid:19) x(x+cos2 x: (10 points) estimate a solution of the equation. = 2. 95 by using the linearization of f (x) = 2x2+1. First, nd the equation of the tangent line.