5.2 Exercises

From Förberedande kurs i matematik 1

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===Exercise 5.2:1===
===Exercise 5.2:1===
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{| width="100%" cellspacing="10px"
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|a)
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|width="100%" | <math>\tan x(\sin x+1) = 2\tan x\quad ?\quad\sin x+1=2</math>
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|width="100%" | <math>\tan x(\sin x+1) = \tan x\quad ?\quad\sin x+1=1</math>
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|b)
|b)
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|width="100%" | <math>x^2-6x+1=0\quad ?\quad (x-3)^2-9+1=0</math>
|width="100%" | <math>x^2-6x+1=0\quad ?\quad (x-3)^2-9+1=0</math>
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|}
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</div>{{#NAVCONTENT:Solution|Solution 5.2:1}}
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</div>{{#NAVCONTENT:Answer|Answer 5.2:1|Solution a|Solution 5.2:1a|Solution b|Solution 5.2:1b|Solution c|Solution 5.2:1c}}
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===Exercise 5.2:2===
===Exercise 5.2:2===
<div class="ovning">
<div class="ovning">
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Criticize the following excerpt from a solution made by a student.
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Criticize the following excerpt from a solution written by a student.
[[Image:ex5_2_2_orig.png||center]]
[[Image:ex5_2_2_orig.png||center]]
</div>{{#NAVCONTENT:Solution|Solution 5.2:2}}
</div>{{#NAVCONTENT:Solution|Solution 5.2:2}}
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===Exercise 5.2:3===
===Exercise 5.2:3===
<div class="ovning">
<div class="ovning">
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Criticize the following excerpt from a solution made by a student.
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Criticize the following excerpt from a solution written by a student.
[[Image:ex5_2_3_orig.png||center]]
[[Image:ex5_2_3_orig.png||center]]
</div>{{#NAVCONTENT:Solution|Solution 5.2:3}}
</div>{{#NAVCONTENT:Solution|Solution 5.2:3}}
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===Exercise 5.2:4===
===Exercise 5.2:4===
<div class="ovning">
<div class="ovning">
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Criticize the following excerpt from a solution made by a student.
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Criticize the following excerpt from a solution written by a student.
[[Image:ex5_2_4_orig.png||center]]
[[Image:ex5_2_4_orig.png||center]]
</div>{{#NAVCONTENT:Solution|Solution 5.2:4}}
</div>{{#NAVCONTENT:Solution|Solution 5.2:4}}
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===Exercise 5.2:5===
===Exercise 5.2:5===
<div class="ovning">
<div class="ovning">
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Criticize the following excerpt from a solution made by a student.
+
Criticize the following excerpt from a solution written by a student.
[[Image:ex5_2_5_orig.png||center]]
[[Image:ex5_2_5_orig.png||center]]
</div>{{#NAVCONTENT:Solution|Solution 5.2:5}}
</div>{{#NAVCONTENT:Solution|Solution 5.2:5}}
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===Exercise 5.2:6===
===Exercise 5.2:6===
<div class="ovning">
<div class="ovning">
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Criticize the following excerpt from a solution made by a student.
+
Criticize the following excerpt from a solution written by a student.
[[Image:ex5_2_6_orig.png||center]]
[[Image:ex5_2_6_orig.png||center]]
</div>{{#NAVCONTENT:Solution|Solution 5.2:6}}
</div>{{#NAVCONTENT:Solution|Solution 5.2:6}}
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===Exercise 5.2:7===
===Exercise 5.2:7===
<div class="ovning">
<div class="ovning">
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Criticize the following excerpt from a solution made by a student.
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Criticize the following excerpt from a solution written by a student.
[[Image:ex5_2_7_orig.png||center]]
[[Image:ex5_2_7_orig.png||center]]
</div>{{#NAVCONTENT:Solution|Solution 5.2:7}}
</div>{{#NAVCONTENT:Solution|Solution 5.2:7}}
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===Exercise 5.2:8===
===Exercise 5.2:8===
<div class="ovning">
<div class="ovning">
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Criticize the following excerpt from a solution made by a student.
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Criticize the following excerpt from a solution written by a student.
[[Image:ex5_2_8_orig.png||center]]
[[Image:ex5_2_8_orig.png||center]]
</div>{{#NAVCONTENT:Solution|Solution 5.2:8}}
</div>{{#NAVCONTENT:Solution|Solution 5.2:8}}
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===Exercise 5.2:9===
===Exercise 5.2:9===
<div class="ovning">
<div class="ovning">
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Criticize the following excerpt from a solution made by a student.
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Criticize the following excerpt from a solution written by a student.
[[Image:ex5_2_9_orig.png||center]]
[[Image:ex5_2_9_orig.png||center]]
</div>{{#NAVCONTENT:Solution|Solution 5.2:9}}
</div>{{#NAVCONTENT:Solution|Solution 5.2:9}}

Current revision

       Theory          Exercises      


Exercise 5.2:1

Which of the arrows \displaystyle \Rightarrow, \displaystyle \Leftarrow or \displaystyle \Leftrightarrow should you insert between the following equations? (Instead of the question mark.)

a) \displaystyle \tan x(\sin x+1) = \tan x\quad ?\quad\sin x+1=1
b) \displaystyle \sqrt{x-1} = x+1\quad ?\quad x-1 = (x+1)^2
c) \displaystyle x^2-6x+1=0\quad ?\quad (x-3)^2-9+1=0

Exercise 5.2:2

Criticize the following excerpt from a solution written by a student.

Exercise 5.2:3

Criticize the following excerpt from a solution written by a student.

Exercise 5.2:4

Criticize the following excerpt from a solution written by a student.

Exercise 5.2:5

Criticize the following excerpt from a solution written by a student.

Exercise 5.2:6

Criticize the following excerpt from a solution written by a student.

Exercise 5.2:7

Criticize the following excerpt from a solution written by a student.

Exercise 5.2:8

Criticize the following excerpt from a solution written by a student.

Exercise 5.2:9

Criticize the following excerpt from a solution written by a student.