W12 Regular

Due date: Sunday 4/5, 11:59pm

Parametric curves

01 $★$

02

Convert parametric curve to function graph

Write the following curves as the graphs of a function $y=f(x)$. (Find $f(x)$ for each case.)

(a) $x=t$, $y=t$ and $-\infty <t<\infty$

(b) $x=e^t$, $y=e^t$ and $-\infty <t<\infty$

Sketch each curve.

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Solution

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02 $★$

03

Convert function graph to parametric curve

Find parametric curves $c(t)=(x(t),y(t))$ whose images are the following graphs:

(a) $y=3x-4$ and $c(0)=(2,2)$

(b) $y=3x-4$ and $c(3)=(2,2)$

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Solution

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Parametric calculus

03

03

Parametric concavity

Find the interval(s) of $t$ on which the parametric curve $c(t)=(t^2,t^3-4t)$ is concave up.

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Solution

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