MATH 153E
QUIZ 6
数学quiz代做 Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced…
Quiz 6 (Total 15p.) Show your work! 数学quiz代做
- (3p.) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. Eliminate the parameter to find a Cartesian equation of the curve.
a) x = ????; y = 1 – cost. 0 ≤ t ≤ 2π.
b) x = ?2; y = ln t .
2. (2p.) Use the graphs of x = f(t) and and y = g(t) to sketch the parametric curve. Indicate with arrows the direction in which the curve is traced as t increases.
- (2p.) Find the points on the curve where the tangent is horizontal or vertical.
x = ?3 − 3?; y = ?2 – 3.
- (3p.) Find the exact length of the curve.
x = ? sin ?; y = tcos ?. 0 ≤ t ≤ 1.
- (3p.) Find the exact area of the surface obtained by rotating the given curve about the x-axis.
