Matt Del C

Question 1

Sned asymptot

Answer 1

Först:
Lim x—> +|- ♾️ f(x)/x

Sedan:
Lim x—> +|- ♾️ (f(x)-kx)

Question 2

Lodrät asymptot

Answer 2

Lim x—> +|- ♾️

Question 3

Kritiska punkter

Answer 3

f’(x)=0

Question 4

Inflexionspunkt

Answer 4

f”(x)=0

Question 5

Konvex

Answer 5

f”(x)>0

Question 6

Konkav

Answer 6

f”(x)<0

Question 7

Tangentens ekvation

Answer 7

y-f(a)=f’(a)(x-a)

Question 8

Normalens ekvation

Answer 8

y-f(a)=-1/(f’(a))(x-a)

Question 9

Volymen för rotationskropp kring y-axeln

Answer 9

V= 2pi〰️x*f(x)dx

Question 10

f(D)=Sqrt(x)

Answer 10

f’(x)=1/(2*sqrt(x))

Question 11

f(D)=lnx

Answer 11

f’(x)=1/x

Question 12

f(D)=sin x

Answer 12

f’(x)=cos x

Question 13

f(D)= cos x

Answer 13

f’(x)= - sinx

Question 14

f(D)=tan x

Answer 14

f’(x)=1+tan^2x=1/(cos^2*x)

Question 15

f(D)=arcsin x

Answer 15

f’(x)=1/(sqrt(1-x^2))

Question 16

f(D)=arccos x

Answer 16

f’(x)=-1/sqrt(1-x^2)

Question 17

f(D)=arctan x

Answer 17

f’(x)=1/(1+x^2)

Question 18

f(I)=1/(x-a)

Answer 18

F(x)=ln|x-a|

Question 19

f(I)=sin x

Answer 19

F(x)=-cos x + C

Question 20

f(I)=cos x

Answer 20

F(x)= sin x + C

Question 21

f(I)= sin kx

Answer 21

F(x)= -(cos*kx)/k + C

Question 22

f(I)= 1/(1+x^2)

Answer 22

F(x)=arctan x +C

Question 23

f(I)=e^kx

Answer 23

F(x)=(e^(kx))/k + C

Question 24

f(I)=1/(sqrt(1-x^2))

Answer 24

F(x)=arcsin x + C

Question 25

f(xI)=ln x

Answer 25

F(x)= x*lnx -x + C

Question 26

Rotationskroppars volym, roterar kring x-axeln

Answer 26

V=pi*(b)〰️(a)[f(x)]^2

Question 27

Volymen av rotationskroppen som roterar krig y-axeln

Answer 27

(b)〰️(a)2pixf(x)

Question 28

Integralen av en rationell funktion

Answer 28

Täljaren högre grad:
T(x)/N(x)=K(x)+R(x)/N(x)

Nämnaren högre grad:
Partialbråksuppdela,
A +Bx+C osv…

Question 29

Udda funktion med symmetriskt intervall [a,-a]

Answer 29

〰️=0

Question 30

f(I)=tan(x)

Answer 30

F(x)=-ln|cosx|

Question 31

f(I)=x^(-1)

Answer 31

F(x)=ln|x|

Question 32

f(I)=1/(x^2)

Answer 32

F(x)=-1/x

Question 33

För att ta reda på C

Answer 33

Få fram en graf kolla när den skär för olika y värden

Question 34

f”(x)=2

Answer 34

Är hela funktionen konvex och det saknas inflextionspunkt

Question 35

Intergrale av 1/(x^2+a^2) dx

Answer 35

=1/a*arctan(x/a)

Question 36

Avståndsfoeln

Answer 36

d=sqrt((x2-x1)^2+(y2-y1)^2)