MAT137Y1 Midterm: 2004 Test 2 solution
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MAT137Y1 Full Course Notes
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Mat 137y, 2004-2005, solutions to term test 2: for the following, simplify your answers unless otherwise instructed. (8%) (i) evaluate lim x 0 cos5x cos3x x2. X, where x < 0, using the de nition of derivative. p (x + h) x h(p (x + h) + p (x + h) + p (x + h) + X (8%) (ii) find the derivative of f (x) = f 0(x) = lim h 0 f (x + h) f (x) h. 2 (8%) (iii) find the equation of the tangent line to the curve 2(x2 + y2)2 = 25(x2 y2) at the point (3,1). 4(x2 + y2) (2x + 2yy0) = 50x 50yy0. Applying newton"s method to f (x) = x4 20, we have. = 2 24 20 x2 = x1 f (x1) f 0(x1) A car leaves an intersection at noon and travels due south at a speed of 80 km/h.
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