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 = 𝑠𝑖𝑛𝑡; y = 1 – cost. 0 ≤ t ≤ 2π.
b) x = 𝑡2; 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 = 𝑡3 − 3𝑡; y = 𝑡2 – 3.
- (3p.) Find the exact length of the curve.
x = 𝑡 sin 𝑡; y = tcos 𝑡. 0 ≤ t ≤ 1.
- (3p.) Find the exact area of the surface obtained by rotating the given curve about the x-axis.
