5. Exercises

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
(Inserted new exercises)
Line 63: Line 63:
===Exercise 5:4===
===Exercise 5:4===
<div class="ovning">
<div class="ovning">
-
Criticize the following excerpts from solutions made by students
+
Criticize the following excerpt from a solution made by a student.
-
{| width="100%" cellspacing="10px"
+
[[Image:ex5_1_4_orig.png||center]]
-
|a)
+
</div>{{#NAVCONTENT:Solution|Solution 5.1:4}}
-
|width="100%" | [[Image:ex5_1_4a_orig_final.png]]
+
-
|-
+
-
|b)
+
-
|width="100%" | [[Image:ex5_1_4b_orig_final.png]]
+
-
|-
+
-
|c)
+
-
|width="100%" | [[Image:ex5_1_4c_orig_final.png]]
+
-
|-
+
-
|d)
+
-
|width="100%" | [[Image:ex5_1_4d_orig_final.png]]
+
-
|}
+
-
</div>{{#NAVCONTENT:Solution a|Solution 5.1:4a|Solution b|Solution 5.1:4b|Solution c|Solution 5.1:4c|Solution d|Solution 5.1:4d}}
+
===Exercise 5:5===
===Exercise 5:5===
<div class="ovning">
<div class="ovning">
-
Criticize the following excerpts from solutions made by students
+
Criticize the following excerpt from a solution made by a student.
-
{| width="100%" cellspacing="10px"
+
[[Image:ex5_1_5_orig.png||center]]
-
|a)
+
</div>{{#NAVCONTENT:Solution|Solution 5.1:5}}
-
|width="100%" | [[Image:ex5_1_5a_orig_final.png]]
+
 
-
|-
+
 
-
|b)
+
===Exercise 5:6===
-
|width="100%" | [[Image:ex5_1_5b_orig_final.png]]
+
<div class="ovning">
-
|-
+
Criticize the following excerpt from a solution made by a student.
-
|c)
+
[[Image:ex5_1_6_orig.png||center]]
-
|width="100%" | [[Image:ex5_1_5c_orig_final.png]]
+
</div>{{#NAVCONTENT:Solution|Solution 5.1:6}}
-
|-
+
 
-
|d)
+
 
-
|width="100%" | [[Image:ex5_1_5d_orig_final.png]]
+
===Exercise 5:7===
-
|}
+
<div class="ovning">
-
</div>{{#NAVCONTENT:Solution a|Solution 5.1:5a|Solution b|Solution 5.1:5b|Solution c|Solution 5.1:5c|Solution d|Solution 5.1:5d}}
+
Criticize the following excerpt from a solution made by a student.
 +
[[Image:ex5_1_7_orig.png||center]]
 +
</div>{{#NAVCONTENT:Solution|Solution 5.1:7}}
 +
 
 +
 
 +
===Exercise 5:8===
 +
<div class="ovning">
 +
Criticize the following excerpt from a solution made by a student.
 +
[[Image:ex5_1_8_orig.png||center]]
 +
</div>{{#NAVCONTENT:Solution|Solution 5.1:8}}
 +
 
 +
 
 +
===Exercise 5:9===
 +
<div class="ovning">
 +
Criticize the following excerpt from a solution made by a student.
 +
[[Image:ex5_1_9_orig.png||center]]
 +
</div>{{#NAVCONTENT:Solution|Solution 5.1:9}}
 +
 
 +
 
 +
===Exercise 5:10===
 +
<div class="ovning">
 +
Criticize the following excerpt from a solution made by a student.
 +
[[Image:ex5_1_10_orig.png||center]]
 +
</div>{{#NAVCONTENT:Solution|Solution 5.1:10}}
 +
 
 +
 
 +
===Exercise 5:11===
 +
<div class="ovning">
 +
Criticize the following excerpt from a solution made by a student.
 +
[[Image:ex5_1_11_orig.png||center]]
 +
</div>{{#NAVCONTENT:Solution|Solution 5.1:11}}

Revision as of 08:42, 27 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


Exercise 5:4

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

Solution
Solution 5.1:4


Exercise 5:5

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

Solution
Solution 5.1:5


Exercise 5:6

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

Solution
Solution 5.1:6


Exercise 5:7

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

Solution
Solution 5.1:7


Exercise 5:8

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

Solution
Solution 5.1:8


Exercise 5:9

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

Solution
Solution 5.1:9


Exercise 5:10

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

Solution
Solution 5.1:10


Exercise 5:11

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

Solution
Solution 5.1:11
Retrieved from "http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php/5._Exercises"