exercise:8f7afdefb9: Difference between revisions
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\newcommand{\mathds}{\mathbb} | \newcommand{\mathds}{\mathbb} | ||
</math></div> | </math></div> | ||
In each of the following, plot the subset of <math>\R^2</math> that consists of all pairs <math>(x, y)</math> | In each of the following, plot the subset of <math>\R^2</math> that consists of all pairs <math>(x, y)</math> | ||
such that the given equation (or conditions) is satisfied. | such that the given equation (or conditions) is satisfied. | ||
<ul style{{=}}"list-style-type:lower-alpha"><li><math>3x + 2y = 3</math></li> | <ul style{{=}}"list-style-type:lower-alpha"><li><math>3x + 2y = 3</math></li> | ||
<li><math>x + y = 1</math></li> | <li><math>x + y = 1</math></li> | ||
| Line 45: | Line 47: | ||
<li><math>y = |x^3|</math></li> | <li><math>y = |x^3|</math></li> | ||
<li><math>y = \mbox{largest integer less than or equal to}\ x</math></li> | <li><math>y = \mbox{largest integer less than or equal to}\ x</math></li> | ||
<li><math>y = \ | <li><math>y = \begin{cases}2x + 3, & x \geq 0 \\ \frac{x^2}{2}, & x < 0.\end{cases}</math></li> | ||
</ul> | </ul> | ||
Latest revision as of 23:41, 22 November 2024
[math]
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\newcommand{\sx}{\item}
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\newcommand{\xlab}{\sxlab}
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\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}
\newcommand{\ddxof}[1]{\frac{d #1}{d x}}
\newcommand{\ddx}{\frac{d}{dx}}
\newcommand{\ddt}{\frac{d}{dt}}
\newcommand{\dydx}{\ddxof y}
\newcommand{\nxder}[3]{\frac{d^{#1}{#2}}{d{#3}^{#1}}}
\newcommand{\deriv}[2]{\frac{d^{#1}{#2}}{dx^{#1}}}
\newcommand{\dist}{\mathrm{distance}}
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\newcommand{\arccsc}{\mathrm{arccsc\:}}
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\newcommand{\arccosh}{\mathrm{arccosh\:}}
\newcommand{\sech}{\mathrm{sech\:}}
\newcommand{\csch}{\mathrm{csch\:}}
\newcommand{\conj}[1]{\overline{#1}}
\newcommand{\mathds}{\mathbb}
[/math]
In each of the following, plot the subset of [math]\R^2[/math] that consists of all pairs [math](x, y)[/math] such that the given equation (or conditions) is satisfied.
- [math]3x + 2y = 3[/math]
- [math]x + y = 1[/math]
- [math]y = |x|[/math]
- [math]y = \sqrt x[/math]
- [math]x^2 + y^2 = 4[/math]
- [math]x^2 + 4y^2 = 4[/math]
- [math]x^2 + y^2 = 1[/math] and [math]y \geq 0[/math]
- [math]4x^2 - y^2 = 4[/math]
- [math]y = 2x^2 + x - 2[/math]
- [math]y = |x^3|[/math]
- [math]y = \mbox{largest integer less than or equal to}\ x[/math]
- [math]y = \begin{cases}2x + 3, & x \geq 0 \\ \frac{x^2}{2}, & x \lt 0.\end{cases}[/math]