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<style>
annotation { display:none }
</style>
<script type="text/javascript"
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=MML_HTMLorMML">
</script>
</head>
<body lang=EN-US >
<div class=WordSection1>
<p class=MsoNormal><span class=PageNumberDAISY><span lang=EN-GB>1</span></span></p>
<h1>Math Sample Document</h1>
<p class=MsoNormal>This is a test of some example math equations. This document
can be used to test how different assistive technologies interact with math
content In addition, the document can be used for demonstrating how to convert
a MS Word document into other formats.</p>
<h2>Information</h2>
<p class=MsoNormal>The following math content was created using the MathType
plug-in for MS Word.</p>
<h3>Basic Math</h3>
<p class=MsoListNumberCxSpFirst >1.<span style='font:7.0pt "Times New Roman"'>
</span><math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
<semantics>
<mrow>
<mfrac>
<mn>7</mn>
<mn>8</mn>
</mfrac>
<mo>+</mo><mfrac>
<mn>3</mn>
<mn>5</mn>
</mfrac>
<mo>=</mo><mi>x</mi></mrow>
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
eB1vgapeWaaSaaaeaacaaI3aaabaGaaGioaaaacqGHRaWkdaWcaaqa
aiaaiodaaeaacaaI1aaaaiabg2da9iaadIhaaaa@3E92@
</annotation>
</semantics>
</math> </p>
<p class=MsoListNumberCxSpLast >2.<span style='font:7.0pt "Times New Roman"'>
</span>Solve for x. </p>
<p class=MsoNormal style='text-indent:.25in'><math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
<semantics>
<mrow>
<mn>.75</mn><mo stretchy='false'>(</mo><mn>3</mn><mo>−</mo><mn>6</mn><mi>x</mi><mo stretchy='false'>)</mo><mo>=</mo><mn>10</mn><mo>+</mo><mo stretchy='false'>(</mo><mn>8</mn><mi>x</mi><mo>−</mo><mn>4</mn><mo stretchy='false'>)</mo></mrow>
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
eB1vgapeGaaiOlaiaaiEdacaaI1aGaaiikaiaaiodacqGHsislcaaI
2aGaamiEaiaacMcacqGH9aqpcaaIXaGaaGimaiabgUcaRiaacIcaca
aI4aGaamiEaiabgkHiTiaaisdacaGGPaaaaa@47A0@
</annotation>
</semantics>
</math></p>
<p class=MsoListNumber >3.<span style='font:7.0pt "Times New Roman"'>
</span>An ant weighs <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
<semantics>
<mrow>
<mn>3</mn><mo>×</mo><msup>
<mrow>
<mn>10</mn></mrow>
<mrow>
<mo>−</mo><mn>6</mn></mrow>
</msup>
</mrow>
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
eB1vgapeGaaG4maiabgEna0kaaigdacaaIWaWaaWbaaSqabeaacqGH
sislcaaI2aaaaaaa@3EB1@
</annotation>
</semantics>
</math> grams, but can lift 16 grams. How many times
their body weight can an ant lift?</p>
<h3>Algebra</h3>
<p class=MsoListNumberCxSpFirst >1.<span style='font:7.0pt "Times New Roman"'>
</span>Simplify the following expression: <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
<semantics>
<mrow>
<mo stretchy='false'>(</mo><mn>3</mn><msup>
<mi>x</mi>
<mn>5</mn>
</msup>
<mo>+</mo><mn>8</mn><msup>
<mi>x</mi>
<mn>3</mn>
</msup>
<mo stretchy='false'>)</mo><mo>−</mo><mo stretchy='false'>(</mo><mn>7</mn><msup>
<mi>x</mi>
<mn>2</mn>
</msup>
<mo>−</mo><mn>6</mn><msup>
<mi>x</mi>
<mn>3</mn>
</msup>
<mo stretchy='false'>)</mo></mrow>
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
eB1vgapeGaaiikaiaaiodacaWG4bWaaWbaaSqabeaacaaI1aaaaOGa
ey4kaSIaaGioaiaadIhadaahaaWcbeqaaiaaiodaaaGccaGGPaGaey
OeI0IaaiikaiaaiEdacaWG4bWaaWbaaSqabeaacaaIYaaaaOGaeyOe
I0IaaGOnaiaadIhadaahaaWcbeqaaiaaiodaaaGccaGGPaaaaa@48C1@
</annotation>
</semantics>
</math> </p>
<p class=MsoListNumberCxSpLast >2.<span style='font:7.0pt "Times New Roman"'>
</span>Consider the function <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
<semantics>
<mrow>
<mi>f</mi><mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo><mo>=</mo><mo>−</mo><mn>1</mn><mo>+</mo><mn>0.5</mn><mi>x</mi></mrow>
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
eB1vgapeGaamOzaiaacIcacaWG4bGaaiykaiabg2da9iabgkHiTiaa
igdacqGHRaWkcaaIWaGaaiOlaiaaiwdacaWG4baaaa@4287@
</annotation>
</semantics>
</math> . For what value of x does <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
<semantics>
<mrow>
<mi>f</mi><mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo><mo>=</mo><mn>0</mn></mrow>
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
eB1vgapeGaamOzaiaacIcacaWG4bGaaiykaiabg2da9iaaicdaaaa@3D8F@
</annotation>
</semantics>
</math> ?</p>
<p class=MsoNormal><span class=PageNumberDAISY><span lang=EN-GB>2</span></span></p>
<p class=MsoListNumber >3.<span style='font:7.0pt "Times New Roman"'>
</span>Given the Quadratic Formula, <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
<semantics>
<mrow>
<mi>x</mi><mo>=</mo><mfrac>
<mrow>
<mo>−</mo><mi>b</mi><mo>±</mo><msqrt>
<mrow>
<msup>
<mi>b</mi>
<mn>2</mn>
</msup>
<mo>−</mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow>
</msqrt>
</mrow>
<mrow>
<mn>2</mn><mi>a</mi></mrow>
</mfrac>
</mrow>
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
eB1vgapeGaamiEaiabg2da9maalaaabaGaeyOeI0IaamOyaiabggla
XoaakaaabaGaamOyamaaCaaaleqabaGaaGOmaaaakiabgkHiTiaais
dacaWGHbGaam4yaaWcbeaaaOqaaiaaikdacaWGHbaaaaaa@457D@
</annotation>
</semantics>
</math> , please solve the following equation <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
<semantics>
<mrow>
<mn>3</mn><msup>
<mi>x</mi>
<mn>2</mn>
</msup>
<mo>+</mo><mn>2</mn><mi>x</mi><mo>−</mo><mn>5</mn><mo>=</mo><mn>0</mn></mrow>
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
eB1vgapeGaaG4maiaadIhadaahaaWcbeqaaiaaikdaaaGccqGHRaWk
caaIYaGaamiEaiabgkHiTiaaiwdacqGH9aqpcaaIWaaaaa@4142@
</annotation>
</semantics>
</math> </p>
<h3>Algebra 2</h3>
<p class=MsoListNumberCxSpFirst >1.<span style='font:7.0pt "Times New Roman"'>
</span>Please solve the following equation: <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
<semantics>
<mrow>
<mo>−</mo><msqrt>
<mrow>
<mi>y</mi><mo>+</mo><mn>15</mn></mrow>
</msqrt>
<mo>=</mo><mo>−</mo><mn>4</mn></mrow>
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
eB1vgapeGaeyOeI0YaaOaaaeaacaWG5bGaey4kaSIaaGymaiaaiwda
aSqabaGccqGH9aqpcqGHsislcaaI0aaaaa@3FAB@
</annotation>
</semantics>
</math> </p>
<p class=MsoListNumberCxSpMiddle >2.<span style='font:7.0pt "Times New Roman"'>
</span>Simplify your answer: <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
<semantics>
<mrow>
<mfrac>
<mrow>
<mn>16</mn><msup>
<mi>x</mi>
<mn>2</mn>
</msup>
<msup>
<mi>y</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mn>14</mn><mi>x</mi><mi>y</mi></mrow>
</mfrac>
<mo>⋅</mo><mn>19</mn><msup>
<mi>x</mi>
<mn>2</mn>
</msup>
<mi>y</mi></mrow>
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
eB1vgapeWaaSaaaeaacaaIXaGaaGOnaiaadIhadaahaaWcbeqaaiaa
ikdaaaGccaWG5bWaaWbaaSqabeaacaaIYaaaaaGcbaGaaGymaiaais
dacaWG4bGaamyEaaaacqGHflY1caaIXaGaaGyoaiaadIhadaahaaWc
beqaaiaaikdaaaGccaWG5baaaa@4824@
</annotation>
</semantics>
</math> </p>
<p class=MsoListNumberCxSpLast >3.<span style='font:7.0pt "Times New Roman"'>
</span>Simplify the following: <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
<semantics>
<mrow>
<mn>3</mn><mo stretchy='false'>(</mo><mo>−</mo><mn>5</mn><mi>i</mi><mo stretchy='false'>)</mo></mrow>
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
eB1vgapeGaaG4maiaacIcacqGHsislcaaI1aGaamyAaiaacMcaaaa@3D3E@
</annotation>
</semantics>
</math>.
Please write your answer as <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
<semantics>
<mrow>
<mi>a</mi><mo>+</mo><mi>b</mi><mi>i</mi></mrow>
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
eB1vgapeGaamyyaiabgUcaRiaadkgacaWGPbaaaa@3C2B@
</annotation>
</semantics>
</math> </p>
<h3>Calculus</h3>
<p class=MsoListNumber >1.<span style='font:7.0pt "Times New Roman"'>
</span>Find the following limits.</p>
<p class=MsoListNumber3CxSpFirst >1.<span style='font:7.0pt "Times New Roman"'>
</span><math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
<semantics>
<mrow>
<munder>
<mrow>
<mi>lim</mi></mrow>
<mrow>
<mi>x</mi><mo>→</mo><mn>1</mn></mrow>
</munder>
<mfrac>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
<mo>−</mo><msup>
<mi>x</mi>
<mn>2</mn>
</msup>
<mo>+</mo><mn>1</mn></mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
<mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow>
</mfrac>
</mrow>
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
eB1vgapeWaaCbeaeaaciGGSbGaaiyAaiaac2gaaSqaaiaadIhacqGH
sgIRcaaIXaaabeaakmaalaaabaGaamiEamaaCaaaleqabaGaaG4maa
aakiabgkHiTiaadIhadaahaaWcbeqaaiaaikdaaaGccqGHRaWkcaaI
XaaabaGaamiEamaaCaaaleqabaGaaGOmaaaakiabgkHiTiaaikdaca
WG4bGaey4kaSIaaGymaaaaaaa@4BF4@
</annotation>
</semantics>
</math> </p>
<p class=MsoListNumber3CxSpLast >2.<span style='font:7.0pt "Times New Roman"'>
</span><math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
<semantics>
<mrow>
<munder>
<mrow>
<mi>lim</mi></mrow>
<mrow>
<mi>x</mi><mo>→</mo><mi>∞</mi></mrow>
</munder>
<mfrac>
<mrow>
<mo>−</mo><msup>
<mi>x</mi>
<mn>2</mn>
</msup>
<mo>+</mo><mn>1</mn></mrow>
<mrow>
<mi>x</mi><mo>+</mo><mn>2</mn></mrow>
</mfrac>
</mrow>
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
eB1vgapeWaaCbeaeaaciGGSbGaaiyAaiaac2gaaSqaaiaadIhacqGH
sgIRcqGHEisPaeqaaOWaaSaaaeaacqGHsislcaWG4bWaaWbaaSqabe
aacaaIYaaaaOGaey4kaSIaaGymaaqaaiaadIhacqGHRaWkcaaIYaaa
aaaa@4721@
</annotation>
</semantics>
</math> </p>
<p class=MsoListNumber >2.<span style='font:7.0pt "Times New Roman"'>
</span>Compute the following: <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
<semantics>
<mrow>
<mstyle displaystyle='true'>
<mrow>
<msubsup>
<mo>∫</mo>
<mn>1</mn>
<mn>2</mn>
</msubsup>
<mrow>
<mi>sin</mi></mrow>
</mrow>
</mstyle><mo stretchy='false'>(</mo><mi>π</mi><mi>x</mi><mo>+</mo><mn>1</mn><mo stretchy='false'>)</mo><mi>d</mi><mi>x</mi></mrow>
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
eB1vgapeWaa8qmaeaaciGGZbGaaiyAaiaac6gaaSqaaiaaigdaaeaa
caaIYaaaniabgUIiYdGccaGGOaGaeqiWdaNaamiEaiabgUcaRiaaig
dacaGGPaGaamizaiaadIhaaaa@46A6@
</annotation>
</semantics>
</math> </p>
<p class=MsoNormal><span class=PageNumberDAISY><span lang=EN-GB>3</span></span></p>
<p class=MsoListNumber >3.<span style='font:7.0pt "Times New Roman"'>
</span>Find the average value of <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
<semantics>
<mrow>
<msup>
<mrow>
<mi>sin</mi></mrow>
<mn>2</mn>
</msup>
<mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo></mrow>
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
eB1vgapeGaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaIYaaaaOGa
aiikaiaadIhacaGGPaaaaa@3EAF@
</annotation>
</semantics>
</math> on <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
<semantics>
<mrow>
<mn>0</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mi>π</mi></mrow>
<annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
eB1vgapeGaaGimaiabgsMiJkaadIhacqGHKjYOcqaHapaCaaa@3F6C@
</annotation>
</semantics>
</math> . </p>
</div>
</body>
</html>