Formler

Question 1

Trigonometriska ettan

Answer 1

cos^2(v) + sin^2 (v) = 1

Question 2

Spegling i x-axeln: cos (-v)

Answer 2

cos (v)

Question 3

Spegling i x-axeln: sin (-v)

Answer 3

-sin (v)

Question 4

Spegling i y-axeln: cos (pi - v)

Answer 4

-cos(v)

Question 5

Spegling i y-axeln: sin (pi - v)

Answer 5

sin (v)

Question 6

Komplementära vinklar: sin (pi/2 - v)

Answer 6

cos (v)

Question 7

Komplementära vinklar: cos (pi/2 - v)

Answer 7

sin(v)

Question 8

Dubbla vinkeln (u=v): cos (2u)

Answer 8

cos^2 (u) - sin^2(v)

Question 9

Dubbla vinkeln (u=v): sin (2u)

Answer 9

2sin(u)cos(v)

Question 10

lim (x)

x–>§

Answer 10

§

Question 11

lim (x^a)

x–>§

Answer 11

§

Question 12

lim (1/x)

x–>o+

Answer 12

+§

Question 13

lim (1/x)

x–>0-

Answer 13

-§

Question 14

lim |x|^-a

x–>0

Answer 14

0

Question 15

Derivatans definition: f’(a)

Answer 15

lim ((f(a+h)-f(a))/h)

h–>0

Question 16

Derivatan av: cos (x)

Answer 16

-sin (x)

Question 17

Derivatan av: sin (x)

Answer 17

cos (x)

Question 18

Derivatan av tan (x)

Answer 18

1+tan^2 (x) eller

1/(cos^2 (x)

Question 19

Medelvärdessatsen

Answer 19

(f(b) - f(a)) / (b-a) = f’(c)

Question 20

Derivatan av invers: (f^-1)’ (x)

Answer 20

1 / (f’(f^-1)(x))

Question 21

Potenslag: a^x * a^y

Answer 21

a^x+y

Question 22

Potenslag: a^x / a^y

Answer 22

a^x-y

Question 23

Potenslag: (a*b)^x

Answer 23

a^x * b^x

Question 24

Potenslag: (a^x)^y

Answer 24

a^x*y

Question 25

loga (1)=

Answer 25

0

Question 26

loga (x) + loga (y)

Answer 26

loga (x*y)

Question 27

loga (x) - loga (y)

Answer 27

loga (x/y)

Question 28

loga (x^y)

Answer 28

y*loga (x)

Question 29

loga (x)

Answer 29

logb (x) / logb (a)

Question 30

ln (x*y)

Answer 30

ln (x) + ln (y)

Question 31

ln (x/y)

Answer 31

ln x - ln y

Question 32

ln x^r

Answer 32

r * ln x

Question 33

Derivatan av: ln x

Answer 33

1/x

Question 34

Derivatan av: a^x

Answer 34

(ln a) * a^x

Question 35

a^x

Answer 35

e^(ln a) * x

Question 36

lim x^n / e^x | x-->§

Answer 36

0 (e^x vinner)

Question 37

``` lim ln(x) / x^n x-->§ ```

Answer 37

0 (x^n vinner)

Question 38

lim x^n * ln x | x-->0+

Answer 38

0 (x^n vinner)

Question 39

lim (1 + x/n)^n | x-->§

Answer 39

e^x

Question 40

Derivatan av: arcsin x

Answer 40

1/ sqrt (1-x^2)

Question 41

Derivatan av arccos x

Answer 41

-(1/ sqrt (1-x^2))

Question 42

Derivatan av: arctan x

Answer 42

1/ (1+x^2)

Question 43

Vertikal asymptot

Answer 43

lim (f(x)) = +-§ | x-->a+

Question 44

Sned asymptot

Answer 44

``` k= gränsvärdet går mot oändligheten ((f(x) / x) m= gränsvärdet går mot oändligheten (f(x) - kx) ```