Noen som gidder hjelpe meg med følgende:
f(x) = x^3 - 16x / 4x^3 - 16x^2
Finn grenseverdien når
lim f(x)
x -> 4
Grenseverdier
Moderators: Aleks855, Gustav, Nebuchadnezzar, Janhaa, DennisChristensen, Emilga
-
frnordgulen
- Pytagoras
- Posts: 7
- Joined: 15/02-2007 11:11
[tex]{\lim }\limits_{x \to 4} \frac{{x^3 - 16x}}{{4x^3 - 16x^2 }}[/tex]
[tex]{\lim }\limits_{x \to 4} \frac{{x(x + 4)(x - 4)}}{{4 \cdot x \cdot x \cdot (x - 4)}}[/tex]
[tex]{\lim }\limits_{x \to 4} \frac{{x + 4}}{{4x}} = \frac{{4 + 4}}{{4 \cdot 4}} = \frac{1}{2}[/tex]
[tex]{\lim }\limits_{x \to 4} \frac{{x(x + 4)(x - 4)}}{{4 \cdot x \cdot x \cdot (x - 4)}}[/tex]
[tex]{\lim }\limits_{x \to 4} \frac{{x + 4}}{{4x}} = \frac{{4 + 4}}{{4 \cdot 4}} = \frac{1}{2}[/tex]