5. Exercises - Revision history

Lina: Removing all content from page

2009-01-27T12:38:27Z

Removing all content from page

←Older revision		Revision as of 12:38, 27 January 2009
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-	__NOTOC__
-	{\| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
-	\| style="border-bottom:1px solid #000" width="5px" \|
-	{{Not selected tab\|[[5. Written presentation and communication of mathematics\|Theory]]}}
-	{{Selected tab\|[[5. Exercises\|Exercises]]}}
-	\| style="border-bottom:1px solid #000" width="100%"\|
-	\|}

-
-	===Exercise 5:1===
-	<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 5:2===
-	<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 5:3===
-	<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}}
-
-
-	===Exercise 5:4===
-	<div class="ovning">
-	Criticize the following excerpt from a solution made by a student.
-	[[Image:ex5_1_4_orig.png\|\|center]]
-	</div>{{#NAVCONTENT:Solution\|Solution 5.1:4}}
-
-
-	===Exercise 5:5===
-	<div class="ovning">
-	Criticize the following excerpt from a solution made by a student.
-	[[Image:ex5_1_5_orig.png\|\|center]]
-	</div>{{#NAVCONTENT:Solution\|Solution 5.1:5}}
-
-
-	===Exercise 5:6===
-	<div class="ovning">
-	Criticize the following excerpt from a solution made by a student.
-	[[Image:ex5_1_6_orig.png\|\|center]]
-	</div>{{#NAVCONTENT:Solution\|Solution 5.1:6}}
-
-
-	===Exercise 5:7===
-	<div class="ovning">
-	Criticize the following excerpt from a solution made by a student.
-	[[Image:ex5_1_7_orig.png\|\|center]]
-	</div>{{#NAVCONTENT:Solution\|Solution 5.1:7}}
-
-
-	===Exercise 5:8===
-	<div class="ovning">
-	Criticize the following excerpt from a solution made by a student.
-	[[Image:ex5_1_8_orig.png\|\|center]]
-	</div>{{#NAVCONTENT:Solution\|Solution 5.1:8}}
-
-
-	===Exercise 5:9===
-	<div class="ovning">
-	Criticize the following excerpt from a solution made by a student.
-	[[Image:ex5_1_9_orig.png\|\|center]]
-	</div>{{#NAVCONTENT:Solution\|Solution 5.1:9}}
-
-
-	===Exercise 5:10===
-	<div class="ovning">
-	Criticize the following excerpt from a solution made by a student.
-	[[Image:ex5_1_10_orig.png\|\|center]]
-	</div>{{#NAVCONTENT:Solution\|Solution 5.1:10}}
-
-
-	===Exercise 5:11===
-	<div class="ovning">
-	Criticize the following excerpt from a solution made by a student.
-	[[Image:ex5_1_11_orig.png\|\|center]]
-	</div>{{#NAVCONTENT:Solution\|Solution 5.1:11}}

Tek: Inserted new exercises

2009-01-27T08:42:10Z

Inserted new exercises

←Older revision		Revision as of 08:42, 27 January 2009
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	===Exercise 5:4===		===Exercise 5:4===
	<div class="ovning">		<div class="ovning">
-	Criticize the following ~~excerpts~~ from ~~solutions~~ made by ~~students~~	+	Criticize the following excerpt from a solution made by a student.
-	~~{\| width="100%" cellspacing="10px"~~	+	[[Image:ex5_1_4_orig.png\|\|center]]
-	\|a)	+	</div>{{#NAVCONTENT:Solution\|Solution 5.1:4}}
-	~~\|width="100%" \| [[Image:ex5_1_4a_orig_final~~.~~png]]~~	+
-	\|-	+
-	~~\|b)~~	+
-	~~\|width="100%" \|~~ [[Image:~~ex5_1_4b_orig_final~~.png]]	+
-	\|-	+
-	\|c)	+
-	~~\|width="100%" \| [[Image:ex5_1_4c_orig_final.png~~]]	+
-	\|-	+
-	~~\|d)~~	+
-	~~\|width="100%" \| [[Image:ex5_1_4d_orig_final.png]]~~	+
-	\|}	+
-	</div>{{#NAVCONTENT:Solution ~~a\|Solution 5.1:4a\|Solution b\|Solution 5.1:4b\|Solution c\|Solution 5.1:4c\|Solution d~~\|Solution 5.1:4d}}	+


	===Exercise 5:5===		===Exercise 5:5===
	<div class="ovning">		<div class="ovning">
-	Criticize the following ~~excerpts~~ from ~~solutions~~ made by ~~students~~	+	Criticize the following excerpt from a solution made by a student.
-	{\| ~~width~~=~~"100%" cellspacing~~="~~10px~~"	+	[[Image:ex5_1_5_orig.png\|\|center]]
-	\|a)	+	</div>{{#NAVCONTENT:Solution\|Solution 5.1:5}}
-	~~\|width="100%" \|~~ [[Image:~~ex5_1_5a_orig_final~~.png]]	+
-	\|-	+
-	~~\|b)~~	+	===Exercise 5:6===
-	~~\|width~~="~~100%~~" \| [[Image:~~ex5_1_5b_orig_final~~.png]]	+	<div class="ovning">
-	\|-	+	Criticize the following excerpt from a solution made by a student.
-	~~\|c)~~	+	[[Image:ex5_1_6_orig.png\|\|center]]
-	~~\|width~~="~~100%~~" \| [[Image:~~ex5_1_5c_orig_final~~.png]]	+	</div>{{#NAVCONTENT:Solution\|Solution 5.1:6}}
-	\|-	+
-	~~\|d)~~	+
-	~~\|width~~="~~100%~~" \| [[Image:~~ex5_1_5d_orig_final~~.png]]	+	===Exercise 5:7===
-	\|}	+	<div class="ovning">
-	</div>{{#NAVCONTENT:Solution a\|Solution 5.1:~~5a\|Solution b\|Solution~~ 5.1:5b\|Solution c\|Solution 5.1:5c\|Solution d\|Solution 5.1:5d}}	+	Criticize the following excerpt from a solution made by a student.
		+	[[Image:ex5_1_7_orig.png\|\|center]]
		+	</div>{{#NAVCONTENT:Solution\|Solution 5.1:7}}
		+
		+
		+	===Exercise 5:8===
		+	<div class="ovning">
		+	Criticize the following excerpt from a solution made by a student.
		+	[[Image:ex5_1_8_orig.png\|\|center]]
		+	</div>{{#NAVCONTENT:Solution\|Solution 5.1:8}}
		+
		+
		+	===Exercise 5:9===
		+	<div class="ovning">
		+	Criticize the following excerpt from a solution made by a student.
		+	[[Image:ex5_1_9_orig.png\|\|center]]
		+	</div>{{#NAVCONTENT:Solution\|Solution 5.1:9}}
		+
		+
		+	===Exercise 5:10===
		+	<div class="ovning">
		+	Criticize the following excerpt from a solution made by a student.
		+	[[Image:ex5_1_10_orig.png\|\|center]]
		+	</div>{{#NAVCONTENT:Solution\|Solution 5.1:10}}
		+
		+
		+	===Exercise 5:11===
		+	<div class="ovning">
		+	Criticize the following excerpt from a solution made by a student.
		+	[[Image:ex5_1_11_orig.png\|\|center]]
		+	</div>{{#NAVCONTENT:Solution\|Solution 5.1:11}}

Tek at 15:01, 26 January 2009

2009-01-26T15:01:35Z

←Older revision		Revision as of 15:01, 26 January 2009
Line 59:		Line 59:
	\|}		\|}
	</div>{{#NAVCONTENT:Answer\|Answer 5.1:3}}		</div>{{#NAVCONTENT:Answer\|Answer 5.1:3}}
		+
		+
		+	===Exercise 5:4===
		+	<div class="ovning">
		+	Criticize the following excerpts from solutions made by students
		+	{\| width="100%" cellspacing="10px"
		+	\|a)
		+	\|width="100%" \| [[Image:ex5_1_4a_orig_final.png]]
		+	\|-
		+	\|b)
		+	\|width="100%" \| [[Image:ex5_1_4b_orig_final.png]]
		+	\|-
		+	\|c)
		+	\|width="100%" \| [[Image:ex5_1_4c_orig_final.png]]
		+	\|-
		+	\|d)
		+	\|width="100%" \| [[Image:ex5_1_4d_orig_final.png]]
		+	\|}
		+	</div>{{#NAVCONTENT:Solution a\|Solution 5.1:4a\|Solution b\|Solution 5.1:4b\|Solution c\|Solution 5.1:4c\|Solution d\|Solution 5.1:4d}}
		+
		+
		+	===Exercise 5:5===
		+	<div class="ovning">
		+	Criticize the following excerpts from solutions made by students
		+	{\| width="100%" cellspacing="10px"
		+	\|a)
		+	\|width="100%" \| [[Image:ex5_1_5a_orig_final.png]]
		+	\|-
		+	\|b)
		+	\|width="100%" \| [[Image:ex5_1_5b_orig_final.png]]
		+	\|-
		+	\|c)
		+	\|width="100%" \| [[Image:ex5_1_5c_orig_final.png]]
		+	\|-
		+	\|d)
		+	\|width="100%" \| [[Image:ex5_1_5d_orig_final.png]]
		+	\|}
		+	</div>{{#NAVCONTENT:Solution a\|Solution 5.1:5a\|Solution b\|Solution 5.1:5b\|Solution c\|Solution 5.1:5c\|Solution d\|Solution 5.1:5d}}

Lina at 13:04, 22 January 2009

2009-01-22T13:04:39Z

←Older revision		Revision as of 13:04, 22 January 2009
Line 38:		Line 38:
	x&=n\pi\cr		x&=n\pi\cr
	x&=\displaystyle \frac{\pi}{4}+\displaystyle \frac{n\pi}{2}		x&=\displaystyle \frac{\pi}{4}+\displaystyle \frac{n\pi}{2}
-	}\right</math>	+	}\right.</math>
	\|d)		\|d)
	\|\| <math>\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\ \sqrt{2 + \sqrt{4}}</math>		\|\| <math>\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\ \sqrt{2 + \sqrt{4}}</math>

Lina at 13:04, 22 January 2009

2009-01-22T13:04:01Z

←Older revision		Revision as of 13:04, 22 January 2009
Line 23:		Line 23:
	\|}		\|}
	</div>{{#NAVCONTENT:Answer\|Answer 5.1:1}}		</div>{{#NAVCONTENT:Answer\|Answer 5.1:1}}
		+

	===Exercise 5:2===		===Exercise 5:2===
Line 29:		Line 30:
	{\| 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>\cos{v} = \cos{\displaystyle \frac{3\pi}{2}}</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>\tan\displaystyle\frac{u}{2}=\frac{\sin u}{1+\cos u}</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>\left\{\eqalign{
		+	x&=n\pi\cr
		+	x&=\displaystyle \frac{\pi}{4}+\displaystyle \frac{n\pi}{2}
		+	}\right</math>
	\|d)		\|d)
-	\|\| <math>\~~displaystyle~~ \~~frac{1}{1+~~\~~displaystyle~~ \~~frac~~{~~1}{1~~+\~~displaystyle \frac~~{~~1}{1+x}~~}}</math>	+	\|\| <math>\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\ \sqrt{2 + \sqrt{4}}</math>
	\|}		\|}
	</div>{{#NAVCONTENT:Answer\|Answer 5.1:2}}		</div>{{#NAVCONTENT:Answer\|Answer 5.1:2}}
-

	===Exercise 5:3===		===Exercise 5:3===
Line 46:		Line 49:
	{\| 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>x^3y^2\left(\displaystyle \frac{1}{y} - \frac{1}{xy}+1\right)</math>
	\|b)		\|b)
-	\|width="50%" \| <math>\~~tan~~\displaystyle\frac{u}{2}=\frac{~~\sin u~~}{1+\~~cos u}~~</math>	+	\|width="50%" \| <math>\left(x-y+\displaystyle\frac{x^2}{y-x}\right) \left(\displaystyle\frac{y}{2x-y}-1\right)</math>
	\|-		\|-
	\|c)		\|c)
-	\|\| <math>\~~left~~\{~~\eqalign{~~	+	\|\| <math>\displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2}</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>\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+x}}}</math>
	\|}		\|}
	</div>{{#NAVCONTENT:Answer\|Answer 5.1:3}}		</div>{{#NAVCONTENT:Answer\|Answer 5.1:3}}

Lina at 13:00, 22 January 2009

2009-01-22T13:00:29Z

←Older revision		Revision as of 13:00, 22 January 2009
Line 56:		Line 56:
	}\right.</math>		}\right.</math>
	\|d)		\|d)
-	\|\| <math>~~\sqrt{2 + \sqrt{4}}~~\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\</math>	+	\|\| <math>\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\ \sqrt{2 + \sqrt{4}}</math>
	\|}		\|}
	</div>{{#NAVCONTENT:Answer\|Answer 5.1:3}}		</div>{{#NAVCONTENT:Answer\|Answer 5.1:3}}

Lina at 12:59, 22 January 2009

2009-01-22T12:59:23Z

←Older revision		Revision as of 12:59, 22 January 2009
Line 56:		Line 56:
	}\right.</math>		}\right.</math>
	\|d)		\|d)
-	\|\| <math>\~~sqrt2~~\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\</math>	+	\|\| <math>\sqrt{2 + \sqrt{4}}\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\</math>
	\|}		\|}
	</div>{{#NAVCONTENT:Answer\|Answer 5.1:3}}		</div>{{#NAVCONTENT:Answer\|Answer 5.1:3}}

Lina at 12:57, 22 January 2009

2009-01-22T12:57:10Z

←Older revision		Revision as of 12:57, 22 January 2009
Line 29:		Line 29:
	{\| width="100%" cellspacing="10px"		{\| width="100%" cellspacing="10px"
	\|a)		\|a)
-	\|width="50%" \| <math>\displaystyle\frac{~~a+b~~}{d-c}</math>	+	\|width="50%" \| <math>x^3y^2\left(\displaystyle \frac{1}{y} - \frac{1}{xy}+1\right)</math>
	\|b)		\|b)
-	\|width="50%" \| <math>\~~sqrt~~{3}</math>	+	\|width="50%" \| <math>\left(x-y+\displaystyle\frac{x^2}{y-x}\right) \left(\displaystyle\frac{y}{2x-y}-1\right)</math>
	\|-		\|-
	\|c)		\|c)
-	\|\| <math>4x^2 - x</math>	+	\|\| <math>\displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2}</math>
	\|d)		\|d)
-	\|\| <math>\~~sin^2 x~~ + \~~cos~~ x</math>	+	\|\| <math>\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+x}}}</math>
	\|}		\|}
	</div>{{#NAVCONTENT:Answer\|Answer 5.1:2}}		</div>{{#NAVCONTENT:Answer\|Answer 5.1:2}}
Line 46:		Line 46:
	{\| width="100%" cellspacing="10px"		{\| width="100%" cellspacing="10px"
	\|a)		\|a)
-	\|width="50%" \| <math>\displaystyle\frac{~~a+b~~}{~~d-c~~}</math>	+	\|width="50%" \| <math>\cos{v} = \cos{\displaystyle \frac{3\pi}{2}}</math>
	\|b)		\|b)
-	\|width="50%" \| <math>\~~sqrt~~{3}</math>	+	\|width="50%" \| <math>\tan\displaystyle\frac{u}{2}=\frac{\sin u}{1+\cos u}</math>
	\|-		\|-
	\|c)		\|c)
-	\|\| <math>~~4x^2 -~~ x</math>	+	\|\| <math>\left\{\eqalign{
		+	x&=n\pi\cr
		+	x&=\displaystyle \frac{\pi}{4}+\displaystyle \frac{n\pi}{2}
		+	}\right.</math>
	\|d)		\|d)
-	\|\| <math>\~~sin~~^~~2 x +~~ \~~cos x~~</math>	+	\|\| <math>\sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\</math>
	\|}		\|}
	</div>{{#NAVCONTENT:Answer\|Answer 5.1:3}}		</div>{{#NAVCONTENT:Answer\|Answer 5.1:3}}

Lina at 12:46, 22 January 2009

2009-01-22T12:46:23Z

←Older revision		Revision as of 12:46, 22 January 2009
Line 10:		Line 10:
	===Exercise 5:1===		===Exercise 5:1===
	<div class="ovning">		<div class="ovning">
-	Write the formulas in TeX	+	Write the formulas in TeX , you can test your text in the editor to your individual assignment.
	{\| width="100%" cellspacing="10px"		{\| width="100%" cellspacing="10px"
	\|a)		\|a)

Lina at 12:44, 22 January 2009

2009-01-22T12:44:45Z

←Older revision		Revision as of 12:44, 22 January 2009
Line 23:		Line 23:
	\|}		\|}
	</div>{{#NAVCONTENT:Answer\|Answer 5.1:1}}		</div>{{#NAVCONTENT:Answer\|Answer 5.1:1}}
-

	===Exercise 5:2===		===Exercise 5:2===
	<div class="ovning">		<div class="ovning">
-	~~Simplify~~	+	Write the formulas in TeX
		+	{\| 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 5.1:2}}
		+
		+
		+	===Exercise 5:3===
		+	<div class="ovning">
		+	Write the formulas in TeX
	{\| width="100%" cellspacing="10px"		{\| width="100%" cellspacing="10px"
	\|a)		\|a)
-	\|width="50%"\| <math>(3-~~(7-4))(6-5)~~</math>	+	\|width="50%" \| <math>\displaystyle\frac{a+b}{d-c}</math>
	\|b)		\|b)
-	\|width="50%"\| <math>3~~-(((7-4)+6)-5)~~</math>	+	\|width="50%" \| <math>\sqrt{3}</math>
	\|-		\|-
	\|c)		\|c)
-	\|\| <math>~~3\cdot(~~-~~7)-4\cdot(6-5)~~</math>	+	\|\| <math>4x^2 - x</math>
	\|d)		\|d)
-	\|\| <math>3\~~cdot(-7)-(4~~+~~6)/(-5)~~</math>	+	\|\| <math>\sin^2 x + \cos x</math>
	\|}		\|}
-	</div>{{#NAVCONTENT:Answer\|Answer 5.1:~~2\|Solution a\|Solution 5.1:2a\|Solution b\|Solution 5.1:2b\|Solution c\|Solution 5.1:2c\|Solution d\|Solution 5.1:2d~~}}	+	</div>{{#NAVCONTENT:Answer\|Answer 5.1:3}}