APPM 1340 Final: appm1340fall2014examfinal_sol
Document Summary
1. (a) (10 points) find dy/dx given y sin x = x + y2. Solution: y sin x = x + y2 y cos x + sin x sin x dy dx 2y (sin x 2y) dy dx dy dx dy dx dy dx. 1 y cos x sin x 2y (b) (16 points) let f (x) = csc2(2x) and g(x) = cot2(2x): find an equation for the line tangent to y = f (x) at x = . 4 : find an equation for the line tangent to y = g(x) at x = . Solution: f (x) = 2 csc(2x)( 2 csc(2x) cot(2x)) = 4 csc2(2x) cot(2x) f ( f ( . 4 ) or y = 1 : g (x) = 2 cot(2x)( 2 csc2(2x)) = 4 cot(2x) csc2(2x) = f (x) 4 ) = 0, the tangent line is y = f ( g ( g( .
