L I M I E T E N   met
meerdere wortelvormen

LIMITS   (involving root forms)
40o\(\displaystyle \underset {\underset {<     }{x \to {- \frac{\sqrt2}{2}}}} {\lim} \:{\frac{\sqrt 2 - 3x}{\sqrt 2\,x + 1}}\) 41o\( \displaystyle \underset {\underset {< }{x \to 1}} {\lim} \: \frac{\sqrt {1-x}}{\sqrt {1-x^2}} \)
42o\(\displaystyle \lim_{x \to 1} \: \frac{\sqrt {2-2x}}{\sqrt {1 - x^2}}\) 43o\(\large \frac {\sqrt {h\,+\,2}\:-\:\sqrt 2} {h\,\sqrt 2} \)
44r\(\displaystyle \lim_{x \to a} \: \frac{x\sqrt x-a\sqrt a}{\sqrt x - \sqrt a }\) 45o\(\displaystyle \lim_{x \to 0} \: \frac{\sqrt {4+x}-\sqrt {4-x} }{x}\)
46r\(\displaystyle \lim_{x \to 1} \: \frac{x^2-\sqrt x}{\sqrt x - 1}\) 47r\(\small\displaystyle \lim_{x \to 0} \: \frac{\sqrt{4+x}+\sqrt{4-x}-4}{x}\)
48r\(\displaystyle \lim_{x \to 1} \: \frac{ \sqrt[3]x - 1}{\sqrt x - 1}\) 49r\(\displaystyle \lim_{x \to 2} \: \frac{ x-\sqrt{8-x^2}}{3x-x\sqrt{1+2x^2}}\)
50r\(\displaystyle \lim_{x \to 2} \: \frac{ \frac{1}{\sqrt x}- \frac{1}{\sqrt 2}}{x-2}\) 51o\(\displaystyle \lim_{x \to 0}\: \frac{\sqrt{1+x}-1}{x}\)
52r \(\displaystyle\!\lim_{x \to 1}\frac{x^\frac14-1}{x^\frac13-1}\) new 53r \(\displaystyle\!\lim_{x \to 1}\frac{\sqrt[6]{x-1}}{\sqrt{x-1}}\) new
54o\(\displaystyle \lim_{x \to -\infty}\: \left ( \sqrt{x^2+5x}-\sqrt{x^2+x} \right )\)
55o\(\scriptsize \displaystyle \lim_{x \to \infty}\: \frac{x+\sqrt{x^2+1}}{x}-\displaystyle \lim_{x \to -\infty}\: \frac{x+\sqrt{x^2+1}}{x}\)
56r\(\small \displaystyle \lim_{x \to +\infty}\: \left ( \sqrt{x^2+1}-\sqrt{x^3+1} \right )\)
57r\(\small \displaystyle \lim_{x \to 0}\: \frac{\sqrt{a+bx}-\sqrt 3}{x}=\sqrt{3}\)
58r\(\small \displaystyle \lim_{x \to -2}\: \frac{\sqrt{1+\sqrt{x+6}}-\sqrt 3}{x+2}\)
59r functie continu maken
60r \(\small \displaystyle \lim_{x \to\,0}\: \frac{\sqrt{x+64}-8}{\sqrt[3]{x+64}-4}\) nieuw
61r \(\small \displaystyle \lim_{x \to 1}\: \frac{ \sqrt{2\!+\!\sqrt{x+3}}-\!2}{x-1}\) nieuw
62r \(\small \displaystyle \lim_{x\to\,4}\frac{\sqrt{x^2+9}-5}{\sqrt{3x-3}-3}\) nieuw
63r\(\small\displaystyle\lim_{x\to\,0}\frac{\sqrt x}{\sqrt{x+\sqrt{x+\sqrt x}}}\) nieuw
64r\(\small\displaystyle\lim_{x\to+\infty}\left(\frac{\sqrt{x-2}}{\sqrt{x+2}}\cdot x-x\right)\) nieuw
65r\(\small\displaystyle\lim_{x\to\,0}\frac{\sqrt{2+\sqrt{1+x^4}}-\sqrt3}{x^4}\) nieuw
66r\(\small\displaystyle\lim_{x\to+\infty}\frac{\sqrt{64x^2+4}-\sqrt{9x^2+5}}{x+\sqrt{x^2+x}}\) nieuw
67r\(\small\displaystyle\lim_{x\to0}\frac{\sqrt{1-x^2}-\sqrt{1+x^2}}{2x^2}\) nieuw

➔ 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 11 aug 2024 ←