5.1 Exercises

From Förberedande kurs i matematik 1

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(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...)
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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>
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|width="50%" | <math>2-3+4</math>
|b)
|b)
-
|width="50%" | <math>\sqrt{3}</math>
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|width="50%" | <math>-1+0.3</math>
|-
|-
|c)
|c)
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|| <math>4x^2 - x</math>
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|| <math>-5-(-3)=-5+3</math>
|d)
|d)
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|| <math>\sin^2 x + \cos x</math>
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|| <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>
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|width="50%" | <math>4x^2-\sqrt{x}</math>
|-
|-
|c)
|c)
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|| <math>\left\{\eqalign{
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|| <math>4\times 3^n\ge n^3</math>
-
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)
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|| <math>\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\ \sqrt{2 + \sqrt{4}}</math>
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|| <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}}

Revision as of 14:08, 28 January 2009

       Theory          Exercises      

Exercise 5.1:1

Write the following formulas in LaTeX .

a) \displaystyle 2-3+4 b) \displaystyle -1+0.3
c) \displaystyle -5-(-3)=-5+3 d) \displaystyle 5/2+1 > 5/(2+1)
Answer
Answer 5.1:1


Exercise 5.1:2

Write the following formulas in LaTeX.

a) \displaystyle 3\times 4\pm 4 b) \displaystyle 4x^2-\sqrt{x}
c) \displaystyle 4\times 3^n\ge n^3 d) \displaystyle 3-(5-2)=-(-3+5-2)
Answer
Answer 5.1:2

Exercise 5.1:3

Write the following formulas in LaTeX

a) \displaystyle \dfrac{x+1}{x^2-1} = \dfrac{1}{x-1} b) \displaystyle \left(\dfrac{5}{x}-1\right)(1-x)
c) \displaystyle \dfrac{\frac{1}{2}}{\frac{1}{3}+\frac{1}{4}} d) \displaystyle \dfrac{1}{1+\dfrac{1}{1+x}}
Answer
Answer 5.1:3

Exercise 5.1:4

Write the following formulas in LaTeX

a) \displaystyle \sin^2 x+\cos x b) \displaystyle \cos v=\cos\dfrac{3\pi}{2}
c) \displaystyle \cot 2x=\dfrac{1}{\tan 2x} d) \displaystyle \tan\dfrac{u}{2}=\dfrac{\sin u}{1+\cos u}
Answer
Answer 5.1:4

Exercise 5.1:5

Write the following formulas in LaTeX

a) \displaystyle \sqrt{4+x^2} b) \displaystyle \sqrt[n]{x+y}\ne\sqrt[n]{x}+\sqrt[n]{y}
c) \displaystyle \sqrt{\sqrt{3}} = \sqrt[4]{3} d) \displaystyle \left(\sqrt[4]{3}\right)^3\sqrt[3]{2+\sqrt{2}}
Answer
Answer 5.1:5

Exercise 5.1:6

Write the following formulas in LaTeX

a) \displaystyle \ln(4\times 3)=\ln 4+\ln 3 b) \displaystyle \ln(4-3)\ne \ln 4-\ln 3
c) \displaystyle \log_{2}4 = \dfrac{\ln 4}{\ln 2} d) \displaystyle 2^{\log_{2}4} = 4
Answer
Answer 5.1:6

Exercise 5.1:7

Correct the following LaTeX maths code.

a) 4^{\frac{3}{4}}(1-(3-4)
b) 2*sqrt(a+b)
c) cotx = \dfrac{1}{2}Sin 20^{o}
Answer
Answer 5.1:7
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