exercise:Ac3037fff0: Difference between revisions

From Stochiki
(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}...")
 
No edit summary
 
Line 32: Line 32:
\newcommand{\mathds}{\mathbb}
\newcommand{\mathds}{\mathbb}
</math></div>
</math></div>
Determine whether or not each of the following
 
functions is integrable over the proposed interval
Determine whether or not each of the following functions is integrable over the proposed interval.
(see Example \ref{exam 8.6.3}).
 
Give a reason for your answer.
Give a reason for your answer.
<ul style{{=}}"list-style-type:lower-alpha"><li></math></li>
 
<ul style{{=}}"list-style-type:lower-alpha"><li><math>\cos \frac1x</math>, over <math>[0,1]</math></li>
<li><math>\frac{x^2+x-2}{x-1}</math>, over <math>[0,1]</math></li>
<li><math>\frac{x^2+x-2}{x-1}</math>, over <math>[0,1]</math></li>
<li><math>\frac{x^2+x-2}{x-1}</math>, over <math>[0,2]</math></li>
<li><math>\frac{x^2+x-2}{x-1}</math>, over <math>[0,2]</math></li>
<li><math>\frac{x^2+x+2}{x-1}</math>, over <math>[0,2]</math>.</li>
<li><math>\frac{x^2+x+2}{x-1}</math>, over <math>[0,2]</math>.</li>
</ul>
</ul>

Latest revision as of 02:23, 25 November 2024

[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} \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}} \newcommand{\arccot}{\mathrm{arccot\:}} \newcommand{\arccsc}{\mathrm{arccsc\:}} \newcommand{\arcsec}{\mathrm{arcsec\:}} \newcommand{\arctanh}{\mathrm{arctanh\:}} \newcommand{\arcsinh}{\mathrm{arcsinh\:}} \newcommand{\arccosh}{\mathrm{arccosh\:}} \newcommand{\sech}{\mathrm{sech\:}} \newcommand{\csch}{\mathrm{csch\:}} \newcommand{\conj}[1]{\overline{#1}} \newcommand{\mathds}{\mathbb} [/math]

Determine whether or not each of the following functions is integrable over the proposed interval.

Give a reason for your answer.

  • [math]\cos \frac1x[/math], over [math][0,1][/math]
  • [math]\frac{x^2+x-2}{x-1}[/math], over [math][0,1][/math]
  • [math]\frac{x^2+x-2}{x-1}[/math], over [math][0,2][/math]
  • [math]\frac{x^2+x+2}{x-1}[/math], over [math][0,2][/math].