uke 43 taylorpolynomer kap 4.9 +4.10

Question 1

formelen for lineær approksimasjon

Answer 1

f(a)+f’(a)(x-a)

Question 2

Feilleddet for lineær approksimasjon

Answer 2

((f’‘(a))/2)*(x-a)^2

Question 3

Taylor polynom definisjonen

Answer 3

f(a)+f’(a)(x-a)+((f’‘(a))/2)(x-a)^2+…+((f^(n+1)(a))/n!)(x-a)^(n+1)

Question 4

stor O-notasjon

Answer 4

f(x)=Pn(x)+O(x-a)^(n+1)

Question 5

maclaurin for e^x

Answer 5

1+x+(x^2)/2!+(x^3)/3!+… +O(x^(n+1))

Question 6

maclaurin for cos x

Answer 6

1-(x^2)/2!+(x^4)/4!-…+(-1)^n*(x^2n)/(2n)+O(x^(2n+2))

Question 7

maclaurin for sin x

Answer 7

1-(x^3)/3!+(x^5)/5!-…+(-1)^n*(x^(2n+1))/(2n+1)+O(x^(2n+2))

Question 8

maclaurin for 1/(1-x)

Answer 8

1+x+x^2+x^3+…+x^n+O(x^(2n+2))

Question 9

maclaurin for ln(1+x)

Answer 9

x-(x^2)/2+(x^3)/3-…+(-1)^(n-1) *(x^n)/(n)+O(x^(2n+2))