B1

Question 1

D sin x

Answer 1

cos x

Question 2

D cos x

Answer 2

-sin x

Question 3

D tan x

Answer 3

1 / cos^2(x)

Question 4

D arcsin x

Answer 4

1 / √1-x2

Question 5

D arccos x

Answer 5

-1 / √1-x2

Question 6

Standard-gränsvärden

Question 7

D arctan x

Answer 7

1 / 1+x2

Question 8

Standard-trianglar

Question 9

ln (0)

Answer 9

-∞ (ej definierat)

Question 10

ln (1)

Answer 10

0

Question 11

ln (<1)

Answer 11

minus

Question 12

ln (e)

Answer 12

1

Question 13

ln (-)

Answer 13

error

Question 14

e

Answer 14

2,72

Question 15

Additionsformler
cos(x+y)
sin (x+y)

Answer 15

cos(x)cos(y)-sin(x)sin(y)
sin(x)cos(y)+cos(x)sin(y)

Question 16

Subtraktionsformler
cos(x-y)
sin(x-y)

Answer 16

cos(x)cos(y)+sin(x)sin(y)
sin(x)cos(y)-cos(x)sin(y)

Question 17

Definiera vad som menas med att “f är deriverbar i punkten a”.

Question 18

Definiera vad som menas med att “f är kontinuerlig i punkten a”.

Question 19

Räkneregler derivata
D(x*y)
D(x/y)
Kedjeregeln

Answer 19

Dxy + xDy
(Dxy - xDy) / (y^2)

Question 20

Logaritmregler
log(x*y)
log(x/y)
log(x^k)

Answer 20

log(x)+log(y)
log(x)-log(y)
k*log(x)

Question 21

Basbyte för logaritmer (s.137)

Question 22

Skriv sin(x) i cos-form
OBS! 2x

Answer 22

cos((π/2)-x)

Question 23

Skriv cos(x) i sin-form
OBS! 2x

Answer 23

sin((π/2)-x)

Question 24

cos(a)=cos(b) <=>

Answer 24

a=(+-)b+2πk

Question 25

sin(a)=sin(b) <=>

Answer 25

a=b+2πk a=π-b+2πk

Question 26

Cirkelns ekvation

Answer 26

vilka är medelpunkterna

Question 27

Ellipsens ekvation

Answer 27

medelpunkterna resp. halvaxlarna

Question 28

log definition

Answer 28

(a-logaritmen) alog(b) = "det tal som a ska upphöjas med för att få b".