## QUIZ 6

### Quiz 6 (Total 15p.) Show your work! 数学quiz代做

1. (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.

1. (2p.) Find the points on the curve where the tangent is horizontal or vertical.

x = 𝑡3 − 3𝑡; y = 𝑡2 – 3.

1. (3p.) Find the exact length of the curve.

x = 𝑡 sin 𝑡; y = tcos 𝑡. 0 ≤ t ≤ 1.

1. (3p.) Find the exact area of the surface obtained by rotating the given curve about the x-axis.

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