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1.2 Übungen

Aus Online Mathematik Brückenkurs 2

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(Translated links into English)
Zeile 25: Zeile 25:
|width="33%"| <math>\displaystyle\frac{x \ln x}{\sin x}</math>
|width="33%"| <math>\displaystyle\frac{x \ln x}{\sin x}</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.2:1|Lösning a|Lösning 1.2:1a|Lösning b|Lösning 1.2:1b|Lösning c|Lösning 1.2:1c|Lösning d|Lösning 1.2:1d|Lösning e|Lösning 1.2:1e|Lösning f|Lösning 1.2:1f}}
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</div>{{#NAVCONTENT:Answer|Svar 1.2:1|Solution a|Lösning 1.2:1a|Solution b|Lösning 1.2:1b|Solution c|Lösning 1.2:1c|Solution d|Lösning 1.2:1d|Solution e|Lösning 1.2:1e|Solution f|Lösning 1.2:1f}}
===Example 1.2:2===
===Example 1.2:2===
Zeile 45: Zeile 45:
|width="33%"| <math>\cos \sqrt{1-x}</math>
|width="33%"| <math>\cos \sqrt{1-x}</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.2:2|Lösning a|Lösning 1.2:2a|Lösning b|Lösning 1.2:2b|Lösning c|Lösning 1.2:2c|Lösning d|Lösning 1.2:2d|Lösning e|Lösning 1.2:2e|Lösning f|Lösning 1.2:2f}}
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</div>{{#NAVCONTENT:Answer|Svar 1.2:2|Solution a|Lösning 1.2:2a|Solution b|Lösning 1.2:2b|Solution c|Lösning 1.2:2c|Solution d|Lösning 1.2:2d|Solution e|Lösning 1.2:2e|Solution f|Lösning 1.2:2f}}
===Example 1.2:3===
===Example 1.2:3===
Zeile 65: Zeile 65:
|width="33%"| <math>x^{\tan x}</math>
|width="33%"| <math>x^{\tan x}</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.2:3|Lösning a|Lösning 1.2:3a|Lösning b|Lösning 1.2:3b|Lösning c|Lösning 1.2:3c|Lösning d|Lösning 1.2:3d|Lösning e|Lösning 1.2:3e|Lösning f|Lösning 1.2:3f}}
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</div>{{#NAVCONTENT:Answer|Svar 1.2:3|Solution a|Lösning 1.2:3a|Solution b|Lösning 1.2:3b|Solution c|Lösning 1.2:3c|Solution d|Lösning 1.2:3d|Solution e|Lösning 1.2:3e|Solution f|Lösning 1.2:3f}}
===Example 1.2:4===
===Example 1.2:4===
Zeile 72: Zeile 72:
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="33%"| <math>\displaystyle\frac{x}{\sqrt{1-x^2}}</math>
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|width="50%"| <math>\displaystyle\frac{x}{\sqrt{1-x^2}}</math>
|b)
|b)
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|width="33%"| <math>x ( \sin \ln x +\cos \ln x )</math>
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|width="50%"| <math>x ( \sin \ln x +\cos \ln x )</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.2:4|Lösning a|Lösning 1.2:4a|Lösning b|Lösning 1.2:4b}}
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</div>{{#NAVCONTENT:Answer|Svar 1.2:4|Solution a|Lösning 1.2:4a|Solution b|Lösning 1.2:4b}}

Version vom 15:38, 21. Aug. 2008

 
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Example 1.2:1

Calculate the derivative of the following functions and write the answer in simplest possible form:

a) cosxsinx b) x2lnx c) x+1x2+1
d) xsinx e) xlnx f) sinxxlnx

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f

Example 1.2:2

Calculate the derivative of the following functions and write the answer in simplest possible form:

a) sinx2 b) ex2+x c) cosx 
d) lnlnx e) x(2x+1)4 f) cos1−x 

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f

Example 1.2:3

Calculate the derivative of the following functions and write the answer in simplest possible form:

a) ln(x+x+1)  b) x−1x+1  c) 1x1−x2
d) sincossinx e) esinx2 f) xtanx

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f

Example 1.2:4

Calculate the second derivative of the following functions and write the answer in simplest possible form:

a) x1−x2 b) x(sinlnx+coslnx)

Answer | Solution a | Solution b

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/1.2_%C3%9Cbungen“