Reknereglar

Grenseverdier

Hans Georg Schaathun

Mai 2016

$$ \begin{align} \lim_{x\to a} f(x) &= F \\ \lim_{x\to a} g(x) &= G \end{align} $$

$$ \begin{align} \lim_{x\to a} [f(x) + g(x)] &= F + G \\ \lim_{x\to a} [f(x) - g(x)] &= F - G \\ \lim_{x\to a} [f(x)g(x)] &= F\cdot G \\ \lim_{x\to a} \frac{f(x)}{g(x)} &= \frac{F}{G}, \quad\text{dersom } G\neq0 \end{align} $$

$$\lim_{x\to a} f(x) = F$$

Konstantar $k\in\mathbb{R}$ og $m,n\in\mathbb{Z}$

$$ \begin{align} \lim_{x\to a} k\cdot f(x) &= k\cdot F \\ \lim_{x\to a} [f(x)]^{\frac{m}{n}} &= F^{\frac{m}{n}} \end{align} $$

$$ \begin{align} \lim_{x\to a} f(x) &= F \\ \lim_{x\to a} g(x) &= G \end{align} $$

$$ \begin{align} f(x)&\le g(x) \quad\text{for alle } x \text{ i eit intervall rundt } a\\ &\Downarrow \\ F&\le G \end{align} $$

Polynom $P(x)$ og $Q(x)$

$$ \begin{align} \lim_{x\to a} P(x) &= P(a) \\ \lim_{x\to a} \frac{P(x)}{Q(x)} &= \frac{P(a)}{Q(a)}, \quad\text{dersom } Q(a)\neq0 \end{align} $$