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Alle oefeningen wiskunde II (OPGELOST), Handelswetenschappen UGent

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Alle OPGELOSTE oefeningen van wiskunde voor bedrijfskundigen II, gegeven door Philippe Carette. Bundel van 101 pagina's waar alle oefeningen opgelost weergegeven worden. Steeds met voldoende tussenstappen, opgaves en grafische weergaves. Deze oefeningen kunnen door schakelstudenten HW en studenten ...

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  • March 10, 2024
  • 101
  • 2023/2024
  • Class notes
  • Philippe carette
  • All classes
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hoofdstuk 1




o 1 .
4




nrinxax
π
=
-


cox = co4 + (00 = 1 + 1 = 2
o




U 4323
-3
2) ta I
64 - 8 56
= C
=
- -

3 I 3 3 3 3 3




3) a = ex Y = ma -

ene = 0 -
1 =




4) =
5
x2 a
3/2
-312 2
. 4312
-2253
x 2 2 43
x ax = -
·
- -




318 4 3 3 3


255
E 2(55 n
2 125 - & A -
-

= = =

3 3 3




!u
&

5)
4
(3x2 4) ax r 3x 2 4
=
x + = au r =
+
U
O 6X
du = Ax
(3x 4)4 1
4)" 13 0 +
12
(3
&
.
+ -
.



- =


Y o 4




7444 2401 256 I 715
-
> 62145
-
-
- - = =

6 4 4 Y U U 8




6)je
π/2
ein 000 (0 Ca +(2 + (a π13 0 + 112
=
-
-

= = =
+ 13




2)
a

=
bgtex =
6glan4
-



bgtan
-
1 = π(4 + π(4 = 2π(4 = T
-
1
x




8 2Een u
4 2
2
π2
in dt - au =
-


coor r =
a
U Y
-



T T

2
πtE 2π
de
-E car du
-

=
-
I
U U

+ 1)2
2


-( cπ2 I


+
π .

πt de
co
-


-


H U 2


2 T 2 2 +
2 2
i
42
-
-
Co + Co = t -

T 4 H Th


T/2 π/2
π/2
2

9) in xdx = (vinx .
sinxax =
f(4 -
Co x) .

sin x dx sin2x +
(0 x = 1
TT12
sin2 x 2002 x
-

-
T12 1
π12
-

=




-ik - 02 du =
-




-
T/2
/**au +
-
π/2
een r

du
= CO0X

= -sinxdx

π/2 3 T12 π/2
-- &
T/2
-
t
3
U
-- coox + CO23X
π12 3
T/2
-
-




casπ (6 +12 Ca T
co-
-



- + t
-

- 0 + 0 + G -O - O
I 3 3

, 2 tan a atana
2 tan a

+(2)
S ·
o dX
(a /2
18)
xe
E
, =


22 + x
&
-
" betan G




&tana e
-"
>
-
Ogtan by tan


(0)
-1 bgtan(tana) -




4 bgtan =
2 -.
L




anax & -


o =

Ggan =
Ggan-6geino =

5 e
T




as) maxis = =- =
Egtan -
I




!glan- , =
π
betan -
d 0
· -
-

O U
3


n3(x)ax
O O 3

f b 2 + -
0 ( 1)
-202 3
-


=
-

xax + < ax = =
-




S 2
G




= 0
!
+ +
9 -
0 =

1
T/2 T/2 π/2


14) sin(x)dx ein( x)ax sin ax Pan ax S
+
x x +

, =
πI2
- cox + -

Cox
O
-cas 0-CC0 + 17) -

C60 T12 + 1000
,



-
- 1 + 1 -
0 + 1 = 3

2



153x + xax
= x (1 + x9)ax
=
9(xa + x ax =
P x x + x ax
+S x a + x x




-- u au
+ ax V

du
= 1 +

=
x2
2xdx




-90'
O 2
2 -312 U 3/2
laa I

+
-
du = t
2 3/2 2 3/2 G
-
I



0 2
-
I (1 + x2/3/2 +
1 ca + xa)3/2
2 3/2 2 312
-
I O



I 1312 2312 16312 4312
t
-
-
D
E


23/2 3/2 S 3/2 3/2



2 2
- + 125
-
8 2 4

3



2 2
-

-4 2 t
105-3
2




-

5 +
2 2 +
355 % =
35 +
22

, canBa
16)
Fan x (6 , Be
(2 , (2) =
Ggtanx ama =
bgtan(tanB) -



6 gtan(tana) =
B




17 / (x + 1) ax
=, x + 2x + dax
=
x ax
+, 2x ax
+Sax
-
4' + 2x + x'
3
-
I -
I




H 23 H
13
- 1)
5 ' !
2 2
+ 4
- -

- + = + + +
5




G 20 56
3 3
30
- +
23 + 2 = +
3 =

15
t
3
t

15
=


15




n8)( = zat 227
(2)
2

2)da tan a- + t(2t 7) ↳
+
+ +
-
-

-

2 2
t




++
4 ta 372
E 2t2 + -5
2
-
- + = -


2 q 2


"


e⑩ ax-Ya
e

n9) x "
2
x Fax
d x"
is
x
ax ax
=
= =

x* 2
L


3

-(n 2 4) 13 1 A
n
+
-


+
-
-

=

-

3 ..3
8



en 5
1 +1 -N na
- A
-



1
-


- + -
t - = -

- 3 24 24 24 24




20)9(x 3x 3x 6x3
- 6
(x x )dx
y
-
2
x
+
2 ax ax x t
+
+
= =
=

I
333
-




-6. - +
6
3
-




3 = I

3
t
216
3
-
27
3


I
-3 72 9
= 3 63 63 H
-


- +
+ =
+
+ =
+




6




Sao 3 adu =su du
2


·f
-2
21) - =

a

u = 2x + 1

en au = 2dx


2 2
2 2
1)
-




1 (213
- -



(2x + 1 5 -
+
<C
= ⑨}

L -
I 2 -
L -
2
-
113


-2
(113)
225 Sae
I 1 I I 9 1 -

=
- -


- t ↳
-
N
= =

2 so -

2 2 50 2 250



=
& 18 =
3

, 22
,
3)x -
'


,
ax = x" ax
= x ax =
x
312
3/25


M
- x

2/3n
2135




-

3 53 - n -
33
se 1




3325 3325
105 3 + 102
5
3 +
-
- -
- =

3




23) ! i
de
-891) + 1
du =

2Ju -




2 de u

du
=




'
=
t +


t
1
-
12
I


-
I


24



-2 Yuau-2) du +
2 en t
t


=
= W

(u
-




-
1

1)2

-


20 -


au +
2 ens

I

1 1)'
2
1)
-
2(t + -
2 + + + 2m)t +


5


1
24(5 2)5 1)
+
-
-
-
4 + + + 2en2 -
2e 1
L




15 19 4 (5 1)
,
4 + 42n2 42n5 + 1
{
L
+
+

+
-
- -




/
2 D & R



-
- 4 -
(5 + 25 + 2) -
8 + 45 + 4 + 42n2 -
42n5 + 1




-
=
1 -
5 -
25 -
2 -
8 + 45 + 4 + 2(6 -
42n5 + 1




1
-
7 + 25 -
425 +


2




aus" ax = Ve
een du =

+ (ide du u

du
=




=
4x

4x
+ 1




4x 1



-" de
= u -




1
au = de x =




I




jusaut j iede 2 den
- du =
-
+ n

U512




-j u
du-2-312 + H du &u e


4
VII "2 112 4 312
-
-



I -
= - V t
64 112 -112 -
3/2
O G O

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