L I M I E T E N  met één wortelvormen
    LIMITS   (involving one root form)
10g\(\displaystyle \lim_{x \to 9} \: {\frac{\sqrt x - 3}{x-9}}\) 11g\( \displaystyle \lim_{x \to 1} \: \frac{x}{x-\sqrt{1+x}} \)
12o\( \displaystyle \underset {\underset {< }{x \to 3}} {\lim} \: \frac{\sqrt{9-x^2}}{3-x} \) 13o\( \displaystyle \lim_{x \to 1} \: \frac{\sqrt{x+3}-2}{x^2-1} \)
14o\(\displaystyle \lim_{x \to 1} \: {\frac{1-\sqrt x}{x^2-1}}\) 15o\(\displaystyle \lim_{x \to 4} \: {\frac{x^2-16}{2-\sqrt x}}\)
16o\(\displaystyle \lim_{x \to 8} \: {\frac{\sqrt[3]{x} - 2}{x-8}}\) 17o\( \displaystyle \underset {\underset {< }{x \to 1}} {\lim} \:{\frac{\sqrt[3]{(x-1)^4}}{2x-2}}\)
18o\(\displaystyle \lim_{x \to +\infty} \: (\sqrt x - x)\) 19o\(\displaystyle \lim_{x \to -\infty} \: (\sqrt{x^2+x} +x)\)
20o \(\displaystyle \lim_{x \to 0} \: \frac{\sqrt[3]{x+1}-1}{x}\) 21o\(\displaystyle \lim_{x \to -\infty} \: (\sqrt{x^2 + x +5} + x)\)
22o\(\displaystyle \lim_{x \to 0} \: {\frac{x}{x-\sqrt{1+x}}}\) 23o\(\displaystyle \lim_{x \to +\infty} \: {\frac{x}{x-\sqrt{1+x}}}\)
24o\(\displaystyle \lim_{x \to 4} \: {\frac{x-4}{\frac{1}{\sqrt x}-\frac 12 }}\)
25o\(\displaystyle \lim_{\underset{>}{x \to 0}}\sqrt[x\:]{\frac{1+x}{1-x}}\) new
26o\(\displaystyle \underset {\underset {< }{x \to 3}} {\lim} \: \frac{\sqrt{(x-3)^2}}{x-3}\)
27o\(\displaystyle \lim_{\underset{>}{x \to 2}}\: \frac{\cos x}{\sqrt{x-2}}\)
28r\( \displaystyle \underset {x \to 16} {\lim} \: \scriptsize \frac{x-16}{{\sqrt[4]{x}-2}} \) 29r\(\displaystyle \lim_{x \to 0} \: \frac {\sqrt[3]{x+1}-1} {x}\)
30r\( \displaystyle \underset {x \to - \infty} {\lim} \: \scriptsize \frac{x+1}{\sqrt{x^2+7}} \)
31r\( \displaystyle \underset {\underset {< }{x \to 5}} {\lim} \: \scriptsize \frac{\sqrt{25-x^2}}{5-x} \)
32r\(\displaystyle\lim_{x\rightarrow\,6}\frac{\sqrt{2x+4}-4}{6\,-\,x}\)new
33r\(\displaystyle\lim_{x\to\,3}\frac{\frac{1}{\sqrt3}-\frac{1}{\sqrt x}}{x-3}\) new
34r\(\displaystyle \lim_{x \to 0} \frac{\sqrt{(x+1)^3}-1}{x}\)
35r\(\displaystyle \lim_{x\to\,6}\frac{2-\sqrt{x-2}}{x^2-36}\) new
40o\(\small\displaystyle \lim_{x \to 1}\frac{\sqrt x - 1}{x - 1}+\displaystyle \lim_{x \to 1}\frac{x^2 - 1}{x - 1} \)
41r \(f(x)=x+\frac{\sqrt{x^2}}{x}\)
42r functie continu maken_1
43r \(\small\displaystyle \lim_{n \to +\infty}\sqrt[n]{\frac{n^2}{3^n+5^n}}\)
44r \(\small\displaystyle \lim_{n \to +\infty}\sqrt[n]{\frac{1}{2^n+4^n}}\)
45r \(\small\displaystyle\lim_{x\to\,0}\;\frac{|x|}{\sqrt{1-\cos x}}\) new
46r \(\scriptsize\displaystyle\!\lim_{n \to +\infty}\left(\sqrt{x^2\!+3x}-\!x\right)\) new
47r \(\scriptsize\displaystyle\!\lim_{n \to +\infty}\left(\sqrt{4x^2\!-2x}-\!2x\right)\) new
48r \(\small\displaystyle\!\lim_{x \to 4}\frac{2x^3-128}{\sqrt x-2}\) new
49r functie continu maken_2
50r \(\small\displaystyle\!\lim_{x\to3}\frac{\sqrt{x+6}-3}{x^3-27}\)

➔ afgeleiden (enkel berekenen)

  derivatives (calculation)

➔ extremumvraagstukken die zonder
afgeleiden kunnen worden opgelost

  extremum problems (without derivatives)

➔ extremumvraagstukken die met
afgeleiden 'moeten' worden opgelost

  extremum problems (with derivatives)

➔ toepassingen afgeleiden (b.v. raaklijn)

  applications derivatives (e.g. tangent line)

➔ max./min. bij goniometrische uitdrukkingen

  max/min for trigonometric expressions

➔ limieten van veeltermbreuken (a) go

  limits of polynomial fractions (a)

➔ limieten van veeltermbreuken (b) or

  limits of polynomial fractions (b)

➔ limieten met één wortelvorm

  limits involving one square root

➔ limieten met meerdere wortelvormen

  limits involving more than one square root

➔ limieten van goniometrische functies

  limits involving trigonometric functions

➔ limieten met logaritme of het getal e

  limits of exponential or logarithmic functions

➔ verticale en horizontale asymptoten

  vertical and horizontal asymptotes

➔ schuine asymptoten - VARIA

  oblique asymptotes - VARIA






→ telling vanaf 10 aug 2024 ←