exercise:Ebcf5c84f1: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\ex}[1]{\item } \newcommand{\sx}{\item} \newcommand{\x}{\sx} \newcommand{\sxlab}[1]{} \newcommand{\xlab}{\sxlab} \newcommand{\prov}[1] {\quad #1} \newcommand{\provx}[1] {\quad \mbox{#1}} \newcommand{\intext}[1]{\quad \mbox{#1} \quad} \newcommand{\R}{\mathrm{\bf R}} \newcommand{\Q}{\mathrm{\bf Q}} \newcommand{\Z}{\mathrm{\bf Z}} \newcommand{\C}{\mathrm{\bf C}} \newcommand{\dt}{\textbf} \newcommand{\goesto}{\rightarrow}...") |
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For each of the following parametrization, | For each of the following parametrization, | ||
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graph is the parametrized curve | graph is the parametrized curve | ||
<ul style{{=}}"list-style-type:lower-alpha"><li><math>P(t) = (t^2,t)</math>, \quad <math>-\infty < t < \infty</math>.</li> | <ul style{{=}}"list-style-type:lower-alpha"><li><math>P(t) = (t^2,t)</math>, \quad <math>-\infty < t < \infty</math>.</li> | ||
<li> | <li> | ||
<math>\dilemma{x=e^{3t},}{y=e^t, & -\infty < t < \infty.}</math></li> | <math>\dilemma{x=e^{3t},}{y=e^t, & -\infty < t < \infty.}</math></li> | ||
<li> | <li> | ||
<math>\dilemma{x=e^t+e^{-t},} | <math>\dilemma{x=e^t+e^{-t},} | ||
{y=e^t-e^{-t}, & -\infty < t < \infty.}</math></li> | {y=e^t-e^{-t}, & -\infty < t < \infty.}</math></li> | ||
</ul> | </ul> | ||
[For | |||
will need in addition to the equation | [For (b) and (c), you will need in addition to the equation <math>F(x,y) = c</math>, the inequality <math>x > 0</math>.] | ||
<math>F(x,y) = c</math>, the inequality <math>x > 0</math>.] | |||
Latest revision as of 20:43, 25 November 2024
[math]
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[/math]
For each of the following parametrization, find an equation [math]F(x,y) = c[/math] whose graph is the parametrized curve
- [math]P(t) = (t^2,t)[/math], \quad [math]-\infty \lt t \lt \infty[/math].
- [math]\dilemma{x=e^{3t},}{y=e^t, & -\infty \lt t \lt \infty.}[/math]
- [math]\dilemma{x=e^t+e^{-t},} {y=e^t-e^{-t}, & -\infty \lt t \lt \infty.}[/math]
[For (b) and (c), you will need in addition to the equation [math]F(x,y) = c[/math], the inequality [math]x \gt 0[/math].]