W13 Regular

Due date: Sunday 4/12, 11:59pm

More parametric calculus

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Parametric arclength

Find the arclength of the curve given parametrically by $x=2t^2$, $y=3t^2-1$ over the time interval $0\le t\le 4$.

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Solution

Solutions---0260-04

02 $★$

05

Minimum speed of a particle

Suppose a travelling particle has position modelled by the parametric curve:

$$c(t)=(t^3-4t,t^2+1)$$

What is the slowest speed of the particle?

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Solution

Solutions---0260-05

Polar curves

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Convert points: Polar to Cartesian

Convert the polar coordinates for these points into Cartesian (rectangular) coordinates:

(a) $(3,\frac{\pi }{6})$ $$ (b) $(-6,\frac{3\pi }{4})$ $$ (c) $(0,\frac{\pi }{5})$ $$ (d) $(5,-\frac{\pi }{2})$

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Solution

Solutions---0270-03

04 $★$

04

Convert equations: Cartesian to Polar

Convert the Cartesian equation to a polar equation. Be sure to simplify.

(a) $x^2+y^2=25$ $$ (b) $x=5$ $$ (c) $y=x^2$

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Solution

Solutions---0270-04