5. Exercises

From Förberedande kurs i matematik 1

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</div>{{#NAVCONTENT:Answer|Answer 5.1:1}}
</div>{{#NAVCONTENT:Answer|Answer 5.1:1}}
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===Exercise 5:2===
===Exercise 5:2===
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{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="50%" | <math>x^3y^2\left(\displaystyle \frac{1}{y} - \frac{1}{xy}+1\right)</math>
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|width="50%" | <math>\cos{v} = \cos{\displaystyle \frac{3\pi}{2}}</math>
|b)
|b)
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|width="50%" | <math>\left(x-y+\displaystyle\frac{x^2}{y-x}\right) \left(\displaystyle\frac{y}{2x-y}-1\right)</math>
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|width="50%" | <math>\tan\displaystyle\frac{u}{2}=\frac{\sin u}{1+\cos u}</math>
|-
|-
|c)
|c)
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|| <math>\displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2}</math>
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|| <math>\left\{\eqalign{
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x&=n\pi\cr
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x&=\displaystyle \frac{\pi}{4}+\displaystyle \frac{n\pi}{2}
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}\right</math>
|d)
|d)
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|| <math>\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+x}}}</math>
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|| <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}}
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===Exercise 5:3===
===Exercise 5:3===
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{| 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)
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|| <math>\left\{\eqalign{
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|| <math>\displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2}</math>
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x&=n\pi\cr
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x&=\displaystyle \frac{\pi}{4}+\displaystyle \frac{n\pi}{2}
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}\right.</math>
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|d)
|d)
-
|| <math>\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\ \sqrt{2 + \sqrt{4}}</math>
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|| <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}}

Revision as of 13:04, 22 January 2009

       Theory          Exercises      


Exercise 5:1

Write the formulas in TeX , you can test your text in the editor to your individual assignment.

a) \displaystyle \displaystyle\frac{a+b}{d-c} b) \displaystyle \sqrt{3}
c) \displaystyle 4x^2 - x d) \displaystyle \sin^2 x + \cos x
Answer
Answer 5.1:1


Exercise 5:2

Write the formulas in TeX

a) \displaystyle \cos{v} = \cos{\displaystyle \frac{3\pi}{2}} b) \displaystyle \tan\displaystyle\frac{u}{2}=\frac{\sin u}{1+\cos u}
c) \displaystyle \left\{\eqalign{

x&=n\pi\cr x&=\displaystyle \frac{\pi}{4}+\displaystyle \frac{n\pi}{2} }\right

d) \displaystyle \bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\ \sqrt{2 + \sqrt{4}}
Answer
Answer 5.1:2

Exercise 5:3

Write the formulas in TeX

a) \displaystyle x^3y^2\left(\displaystyle \frac{1}{y} - \frac{1}{xy}+1\right) b) \displaystyle \left(x-y+\displaystyle\frac{x^2}{y-x}\right) \left(\displaystyle\frac{y}{2x-y}-1\right)
c) \displaystyle \displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2} d) \displaystyle \displaystyle \frac{1}{1+\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+x}}}
Answer
Answer 5.1:3
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