Kapitel 8 Hohere Math 2

Linear approximation L(x) =

f(x0) + f(x0)’(x - x0)

(f · g)′ =

f′g + fg’

(f/g)’=

$$\frac{f^{\prime}g-fg^{\prime}}{g^2}$$

(f ◦ g)′ (x0)=

f′(g(x0)) · g′(x0)

f,g(x) → 0 oder +∞ fur x →a

$$\lim_{x\to a}\frac{f^{\prime}\left(x\right)}{g^{\prime}\left(x\right)}=\lim_{x\to a}\frac{f\left(x\right)}{g\left(x\right)}$$

$$\lim_{x\to0}\frac{\sin\left(x\right)}{x}$$

=1

$$\lim_{x\to0}\frac{cos\left(x\right)-1}{x}$$

=0

$$\lim_{x\to0}\ln\left(x\right)$$

-∞

Taylorpolynom

$$\sum_{k=0}^{n}\frac{f^{(k)}(0)}{k!}\left(x-x_0\right)^{k}$$

Rn(x;x0)=

$$\frac{f^{(n+1)}(\xi)}{(n+1)!}(x-x_0)^{n+1}$$