This quiz tests the work covered in Lecture 20 and corresponds to Section 4.8 of the
textbook Calculus: Single and Multivariable (Hughes-Hallett, Gleason, McCallum et
al.).

There are more web quizzes at Wiley, select Section 8.

There is an interesting applet at http://www.rfbarrow.btinternet.co.uk/htmasa2/Param1.htm which allows you to play with some equations and see how it changes the parametric curve. There is a slightly more general one at http://www.math.ucla.edu/ ronmiech/crew/eugene/java/ParamPlotter/ParamPlotter.html but you must read the instructions to see how to make it work.

There is a good discussion at http://tutorial.math.lamar.edu/AllBrowsers/2414/ParametricEqn.asp with fully worked examples of plotting parametric curves.

Exactly one option must be correct)

*Choice (a) is incorrect*

*Choice (b) is incorrect*

which travels in the wrong direction.

*Choice (c) is correct!*

*Choice (d) is incorrect*

There may be more than one correct answer. (Zero or more options can be correct)

*There is at least one mistake.*

For example, choice (a) should be True.

$\frac{dx}{dt}=\frac{2-1}{1}=1$ and $\frac{dy}{dt}=\frac{3-0}{1}=3$ and the point (2,3) is on the line,

so $x=2+t\phantom{\rule{0.3em}{0ex}},\phantom{\rule{1em}{0ex}}y=3+3t\phantom{\rule{0.3em}{0ex}}.$

*There is at least one mistake.*

For example, choice (b) should be False.

*There is at least one mistake.*

For example, choice (c) should be True.

$\frac{dx}{dt}=\frac{2-1}{1}=1$ and $\frac{dy}{dt}=\frac{3-0}{1}=3$ and the point (1,0) is on the line,

so $x=1+t\phantom{\rule{0.3em}{0ex}},\phantom{\rule{1em}{0ex}}y=3t\phantom{\rule{0.3em}{0ex}}.$

*There is at least one mistake.*

For example, choice (d) should be False.

*Correct!*

*True*If we consider an object moving from (1,0) to (2,3) in one unit of time then

$\frac{dx}{dt}=\frac{2-1}{1}=1$ and $\frac{dy}{dt}=\frac{3-0}{1}=3$ and the point (2,3) is on the line,

so $x=2+t\phantom{\rule{0.3em}{0ex}},\phantom{\rule{1em}{0ex}}y=3+3t\phantom{\rule{0.3em}{0ex}}.$*False*This is not the correct speed for the object in the $y$ direction.*True*If we consider an object moving from (1,0) to (2,3) in one unit of time then

$\frac{dx}{dt}=\frac{2-1}{1}=1$ and $\frac{dy}{dt}=\frac{3-0}{1}=3$ and the point (1,0) is on the line,

so $x=1+t\phantom{\rule{0.3em}{0ex}},\phantom{\rule{1em}{0ex}}y=3t\phantom{\rule{0.3em}{0ex}}.$*False*These are not the correct speeds for the objects in either direction.

Which of the following is the slope of the curve? Exactly one option must be correct)

*Choice (a) is incorrect*

*Choice (b) is correct!*

*Choice (c) is incorrect*

*Choice (d) is incorrect*

At what time(s) is it stopped? Exactly one option must be correct)

*Choice (a) is incorrect*

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is correct!*

$\frac{dy}{dt}=6{t}^{2}+18t-24=6\left({t}^{2}+3t-4\right)=6\left(t-1\right)\left(t+4\right)$

so the particle is stopped at $t=1\phantom{\rule{0.3em}{0ex}}.$