5.2 Exercises
From Förberedande kurs i matematik 1
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===Exercise 5.2:1=== | ===Exercise 5.2:1=== | ||
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Which of the arrows <math>\Rightarrow</math>, <math>\Leftarrow</math> or <math>\Leftrightarrow</math> should you insert between the following equations? (Instead of the question mark.) | |
| - | </div>{{#NAVCONTENT:Solution|Solution 5.2: | + | {| width="100%" cellspacing="10px" |
| - | + | |a) | |
| + | |width="100%" | <math>\tan x(\sin x+1) = \tan x\quad ?\quad\sin x+1=1</math> | ||
| + | |- | ||
| + | |b) | ||
| + | |width="100%" | <math>\sqrt{x-1} = x+1\quad ?\quad x-1 = (x+1)^2</math> | ||
| + | |- | ||
| + | |c) | ||
| + | |width="100%" | <math>x^2-6x+1=0\quad ?\quad (x-3)^2-9+1=0</math> | ||
| + | |} | ||
| + | </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}} | ||
===Exercise 5.2:2=== | ===Exercise 5.2:2=== | ||
<div class="ovning"> | <div class="ovning"> | ||
| - | Criticize the following excerpt from a solution | + | 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"> | ||
| - | Criticize the following excerpt from a solution | + | 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"> | ||
| - | Criticize the following excerpt from a solution | + | 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}} | ||
| - | |||
===Exercise 5.2:5=== | ===Exercise 5.2:5=== | ||
<div class="ovning"> | <div class="ovning"> | ||
| - | Criticize the following excerpt from a solution | + | 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}} | ||
| - | |||
===Exercise 5.2:6=== | ===Exercise 5.2:6=== | ||
<div class="ovning"> | <div class="ovning"> | ||
| - | Criticize the following excerpt from a solution | + | 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}} | ||
| - | |||
===Exercise 5.2:7=== | ===Exercise 5.2:7=== | ||
<div class="ovning"> | <div class="ovning"> | ||
| - | Criticize the following excerpt from a solution | + | 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}} | ||
| - | |||
===Exercise 5.2:8=== | ===Exercise 5.2:8=== | ||
<div class="ovning"> | <div class="ovning"> | ||
| - | Criticize the following excerpt from a solution | + | 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}} | ||
| - | |||
===Exercise 5.2:9=== | ===Exercise 5.2:9=== | ||
<div class="ovning"> | <div class="ovning"> | ||
| - | Criticize the following excerpt from a solution | + | 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 |
Answer
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Solution a
Solution b
Solution c
Exercise 5.2:2
Criticize the following excerpt from a solution written by a student.
Solution
Exercise 5.2:3
Criticize the following excerpt from a solution written by a student.
Solution
Exercise 5.2:4
Criticize the following excerpt from a solution written by a student.
Solution
Exercise 5.2:5
Criticize the following excerpt from a solution written by a student.
Solution
Exercise 5.2:6
Criticize the following excerpt from a solution written by a student.
Solution
Exercise 5.2:7
Criticize the following excerpt from a solution written by a student.
Solution
Exercise 5.2:8
Criticize the following excerpt from a solution written by a student.
Solution
Exercise 5.2:9
Criticize the following excerpt from a solution written by a student.
Solution
