5.1 Exercises - Revision history

Tek at 14:35, 28 January 2009

2009-01-28T14:35:41Z

←Older revision		Revision as of 14:35, 28 January 2009
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	\|}		\|}
	</div>{{#NAVCONTENT:Answer\|Answer 5.1:1}}		</div>{{#NAVCONTENT:Answer\|Answer 5.1:1}}
-

	===Exercise 5.1:2===		===Exercise 5.1:2===

Tek at 14:08, 28 January 2009

2009-01-28T14:08:43Z

←Older revision		Revision as of 14:08, 28 January 2009
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	===Exercise 5.1:1===		===Exercise 5.1:1===
	<div class="ovning">		<div class="ovning">
-	Write the formulas in ~~TeX , you can test your text in the editor to your individual assignment~~.	+	Write the following formulas in LaTeX .
	{\| width="100%" cellspacing="10px"		{\| width="100%" cellspacing="10px"
	\|a)		\|a)
-	\|width="50%" \| <math>~~\displaystyle\frac{a+b}{d~~-c}</math>	+	\|width="50%" \| <math>2-3+4</math>
	\|b)		\|b)
-	\|width="50%" \| <math>~~\sqrt{~~3}</math>	+	\|width="50%" \| <math>-1+0.3</math>
	\|-		\|-
	\|c)		\|c)
-	\|\| <math>~~4x^2~~ - x</math>	+	\|\| <math>-5-(-3)=-5+3</math>
	\|d)		\|d)
-	\|\| <math>~~\sin^~~2 x + ~~\cos x~~</math>	+	\|\| <math>5/2+1 > 5/(2+1)</math>
	\|}		\|}
	</div>{{#NAVCONTENT:Answer\|Answer 5.1:1}}		</div>{{#NAVCONTENT:Answer\|Answer 5.1:1}}
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	===Exercise 5.1:2===		===Exercise 5.1:2===
	<div class="ovning">		<div class="ovning">
-	Write the formulas in ~~TeX~~	+	Write the following formulas in LaTeX.
	{\| width="100%" cellspacing="10px"		{\| width="100%" cellspacing="10px"
	\|a)		\|a)
-	\|width="50%" \| <math>\~~cos{v} = \cos{\displaystyle \frac{3~~\~~pi}{2}}~~</math>	+	\|width="50%" \| <math>3\times 4\pm 4</math>
	\|b)		\|b)
-	\|width="50%" \| <math>~~\tan\displaystyle\frac{u}{~~2}=\~~frac~~{~~\sin u}{1+\cos u~~}</math>	+	\|width="50%" \| <math>4x^2-\sqrt{x}</math>
	\|-		\|-
	\|c)		\|c)
-	\|\| <math>\~~left\{\eqalign{~~	+	\|\| <math>4\times 3^n\ge n^3</math>
-	~~x&=~~n\~~pi\cr~~	+
-	~~x&=\displaystyle \frac{\pi}{4}+\displaystyle \frac{~~n~~\pi}{2}~~	+
-	~~}\right.~~</math>	+
	\|d)		\|d)
-	\|\| <math>~~\bigl(\sqrt[\scriptstyle4]~~3~~\,\bigr~~)^3~~\ \sqrt{2~~ + ~~\sqrt{4}}~~</math>	+	\|\| <math>3-(5-2)=-(-3+5-2)</math>
	\|}		\|}
	</div>{{#NAVCONTENT:Answer\|Answer 5.1:2}}		</div>{{#NAVCONTENT:Answer\|Answer 5.1:2}}
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	===Exercise 5.1:3===		===Exercise 5.1:3===
	<div class="ovning">		<div class="ovning">
-	Write the formulas in ~~TeX~~	+	Write the following formulas in LaTeX
	{\| width="100%" cellspacing="10px"		{\| width="100%" cellspacing="10px"
	\|a)		\|a)
-	\|width="50%" \| <math>~~x^3y^2\left(~~\~~displaystyle \frac~~{1}{y} - \~~frac~~{1}{~~xy}+~~1~~\right)~~</math>	+	\|width="50%" \| <math>\dfrac{x+1}{x^2-1} = \dfrac{1}{x-1}</math>
	\|b)		\|b)
-	\|width="50%" \| <math>\left(~~x-y+\displaystyle~~\~~frac~~{~~x^2~~}{y-x}\right) ~~\left~~(~~\displaystyle\frac{y}{2x~~-~~y}-1\right~~)</math>	+	\|width="50%" \| <math>\left(\dfrac{5}{x}-1\right)(1-x)</math>
	\|-		\|-
	\|c)		\|c)
-	\|\| <math>\~~displaystyle\frac~~{~~a-b+\displaystyle~~\frac{~~b^2~~}{~~a+b~~}}{~~1-\left(\displaystyle~~\frac{~~a-b~~}{a+b}~~\right)^2~~}</math>	+	\|\| <math>\dfrac{\frac{1}{2}}{\frac{1}{3}+\frac{1}{4}}</math>
	\|d)		\|d)
-	\|\| <math>\~~displaystyle \frac~~{1}{1+\~~displaystyle \frac{1}{1+\displaystyle \frac~~{1}{1+x}}}</math>	+	\|\| <math>\dfrac{1}{1+\dfrac{1}{1+x}}</math>
	\|}		\|}
	</div>{{#NAVCONTENT:Answer\|Answer 5.1:3}}		</div>{{#NAVCONTENT:Answer\|Answer 5.1:3}}
		+
		+	===Exercise 5.1:4===
		+	<div class="ovning">
		+	Write the following formulas in LaTeX
		+	{\| width="100%" cellspacing="10px"
		+	\|a)
		+	\|width="50%" \| <math>\sin^2 x+\cos x</math>
		+	\|b)
		+	\|width="50%" \| <math>\cos v=\cos\dfrac{3\pi}{2}</math>
		+	\|-
		+	\|c)
		+	\|\| <math>\cot 2x=\dfrac{1}{\tan 2x}</math>
		+	\|d)
		+	\|\| <math>\tan\dfrac{u}{2}=\dfrac{\sin u}{1+\cos u}</math>
		+	\|}
		+	</div>{{#NAVCONTENT:Answer\|Answer 5.1:4}}
		+
		+	===Exercise 5.1:5===
		+	<div class="ovning">
		+	Write the following formulas in LaTeX
		+	{\| width="100%" cellspacing="10px"
		+	\|a)
		+	\|width="50%" \| <math>\sqrt{4+x^2}</math>
		+	\|b)
		+	\|width="50%" \| <math>\sqrt[n]{x+y}\ne\sqrt[n]{x}+\sqrt[n]{y}</math>
		+	\|-
		+	\|c)
		+	\|\| <math>\sqrt{\sqrt{3}} = \sqrt[4]{3}</math>
		+	\|d)
		+	\|\| <math>\left(\sqrt[4]{3}\right)^3\sqrt[3]{2+\sqrt{2}}</math>
		+	\|}
		+	</div>{{#NAVCONTENT:Answer\|Answer 5.1:5}}
		+
		+	===Exercise 5.1:6===
		+	<div class="ovning">
		+	Write the following formulas in LaTeX
		+	{\| width="100%" cellspacing="10px"
		+	\|a)
		+	\|width="50%" \| <math>\ln(4\times 3)=\ln 4+\ln 3</math>
		+	\|b)
		+	\|width="50%" \| <math>\ln(4-3)\ne \ln 4-\ln 3</math>
		+	\|-
		+	\|c)
		+	\|\| <math>\log_{2}4 = \dfrac{\ln 4}{\ln 2}</math>
		+	\|d)
		+	\|\| <math>2^{\log_{2}4} = 4</math>
		+	\|}
		+	</div>{{#NAVCONTENT:Answer\|Answer 5.1:6}}
		+
		+	===Exercise 5.1:7===
		+	<div class="ovning">
		+	Correct the following LaTeX maths code.
		+	{\| width="100%" cellspacing="10px"
		+	\|a)
		+	\|width="100%" \| <tt>4^{\frac{3}{4}}(1-(3-4)</tt>
		+	\|-
		+	\|b)
		+	\|width="100%" \| <tt>2*sqrt(a+b)</tt>
		+	\|-
		+	\|c)
		+	\|width="100%" \| <tt>cotx = \dfrac{1}{2}Sin 20^{o}</tt>
		+	\|}
		+	</div>{{#NAVCONTENT:Answer\|Answer 5.1:7}}

Lina: New page: NOTOC {| border="0" cellspacing="0" cellpadding="0" height="30" width="100%" | style="border-bottom:1px solid #000" width="5px" | {{Not selected tab|[[5.1 Writing formulas in Te...

2009-01-27T12:30:55Z

New page: __NOTOC__ {| border="0" cellspacing="0" cellpadding="0" height="30" width="100%" | style="border-bottom:1px solid #000" width="5px" |   {{Not selected tab|[[5.1 Writing formulas in Te...

New page

__NOTOC__
{| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
| style="border-bottom:1px solid #000" width="5px" |  
{{Not selected tab|[[5.1 Writing formulas in TeX|Theory]]}}
{{Selected tab|[[5.1 Exercises|Exercises]]}}
| style="border-bottom:1px solid #000" width="100%"|  
|}

===Exercise 5.1:1===
<div class="ovning">
Write the formulas in TeX , you can test your text in the editor to your individual assignment.
{| width="100%" cellspacing="10px"
|a)
|width="50%" | <math>\displaystyle\frac{a+b}{d-c}</math>
|b)
|width="50%" | <math>\sqrt{3}</math>
|-
|c)
|| <math>4x^2 - x</math>
|d)
|| <math>\sin^2 x + \cos x</math>
|}
</div>{{#NAVCONTENT:Answer|Answer 5.1:1}}

===Exercise 5.1:2===
<div class="ovning">
Write the formulas in TeX
{| width="100%" cellspacing="10px"
|a)
|width="50%" | <math>\cos{v} = \cos{\displaystyle \frac{3\pi}{2}}</math>
|b)
|width="50%" | <math>\tan\displaystyle\frac{u}{2}=\frac{\sin u}{1+\cos u}</math>
|-
|c)
|| <math>\left\{\eqalign{
x&=n\pi\cr
x&=\displaystyle \frac{\pi}{4}+\displaystyle \frac{n\pi}{2}
}\right.</math>
|d)
|| <math>\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\ \sqrt{2 + \sqrt{4}}</math>
|}
</div>{{#NAVCONTENT:Answer|Answer 5.1:2}}

===Exercise 5.1:3===
<div class="ovning">
Write the formulas in TeX
{| width="100%" cellspacing="10px"
|a)
|width="50%" | <math>x^3y^2\left(\displaystyle \frac{1}{y} - \frac{1}{xy}+1\right)</math>
|b)
|width="50%" | <math>\left(x-y+\displaystyle\frac{x^2}{y-x}\right) \left(\displaystyle\frac{y}{2x-y}-1\right)</math>
|-
|c)
|| <math>\displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2}</math>
|d)
|| <math>\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+x}}}</math>
|}
</div>{{#NAVCONTENT:Answer|Answer 5.1:3}}

5.1 Exercises - Revision history

Tek at 14:35, 28 January 2009

Tek at 14:08, 28 January 2009

Lina: New page: __NOTOC__ {| border="0" cellspacing="0" cellpadding="0" height="30" width="100%" | style="border-bottom:1px solid #000" width="5px" | {{Not selected tab|[[5.1 Writing formulas in Te...

Lina: New page: NOTOC {| border="0" cellspacing="0" cellpadding="0" height="30" width="100%" | style="border-bottom:1px solid #000" width="5px" | {{Not selected tab|[[5.1 Writing formulas in Te...