Sem13-m150-1207 - M ATH 150 S EMINAR#13 Q UESTIONS Content Section 10.1 Curves Defined by Parametric Equations Section 10.2 Calculus with Parametric

# Sem13-m150-1207 - M ATH 150 S EMINAR#13 Q UESTIONS...

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M ATH 150: S EMINAR #13 Q UESTIONS Content: Section 10.1: Curves Defined by Parametric Equations Section 10.2: Calculus with Parametric Curves (Tangents only) Section 10.3: Polar Coordinates Questions: 1. One of the graphs below is the graph of following parametric equations: x = t + sin 4 t, y = t 2 + cos 3 t Indicate which one. Give reasons for your choice. *2. Find an equation to the tangent line to the curve x = t, y = t 2 - 2 t at the point corresponding to t = 4 . 3. Find an equation of the tangent to the curve x = 1 + t, y = e t 2 , at the point (2 , e ) by two methods: (a) Without eliminating the parameter. (b) First eliminating the parameter. 4. Find an equation of the tangent to the curve x = sin πt, y = t 2 + t at the point (0 , 2) . Then graph the curve and the tangent. *5. Let x = t 2 + 1 , y = e t - 1 . (a) Find dy/dx . (b) Find d 2 y/dx 2 . (c) For which values of t is the curve concave upward? 6. Given the parametric curve x = t ( t 2 - 3) , y = 3( t 2 - 3) . (a) Find the y -intercepts of the curve. (b) Find the points on the curve where the tangent line is horizontal or vertical.
M ATH 150: S EMINAR #13 Q