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# CT2 - W.A.2 Math 262 Fall 2010 1 Find T B for the circular...

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W.A.2 Math 262 Fall 2010 1 Find circumflexnosp2char circumflexnosp2char circumflexnosp2char , , T glyph1197 B for the circular helix cos sin t t t = + + r i j k . Find also the curvature K at any point on the helix. 2.Find the tangent and normal component of acceleration for curve 2 t t e t e = + + r i j k . 3.Consider the following pair of equations 2 2 2 3 2 xy yv y xv u v xy uvx + + = + + = (a) Show that the above equations implicitly define functions y = y(x,u) and v = v(x,u) near the point (1,1,1,1,1) i.e. what condition must be satisfied. (b) Hence compute the partial derivatives y x and v u at (1,1,1,1,1). 4. Consider the surface defined by z xy = (a) Compute the tangent plane to the surface at pt.(1,1,1) (b) Show that the normal line at an arbitrary point P(x 0 , y o , z o ) is perpendicular to the line joining P to the origin. 5. A downhill skier begins his run at a point (9,6) on the (x,y) plane on a hill whose height is given by 2 2 1000

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