L I M I E T E N
met logaritmen en getal e

LIMITS (involving log or Euler's number (e)
10g lim\(\left ( 1+\frac 1x \right )^{x+3} \) 11g \(\frac {n\,+\,1} {n} \) en \( \left(\frac {n\,+\,1} {n}\right)^n \)
12g lim\(\sqrt[x]{x+1}\) 13g lim\(\,\log_3\,(x+1)^2 \)
14g lim\(\log \,(2x) \) 15g lim\(\left( \frac e3 \right)^x\)
20o lim\(\left ( \frac{x\,+\,6}{x} \right )^{3x} \) 21o lim\(\sqrt[x]{x}\)
22o lim\(\left ( \frac{1\,+\,x}{x} \right )^{4-3x}\)
23o lim\(\left ( 1-\frac 3x \right )^{-6x} \) 24o lim\(\left ( 1-\frac 2x \right )^{4x}\)
25o lim\(\left ( \frac{x\,-\,3}{x} \right )^{\frac x2} \) 26o lim\(\left (1- \frac{1}{2x} \right )^{-3x}\)
27o lim\(\;\left ( 1\!-ax \right )^{\frac 1x} \) 28o lim\( (1+x \sqrt2)^{\frac {\sqrt 2} {x}} \)
29o lim\(\sqrt[x-1]{x}\) 30o lim   \( (1+\cos^2 x)^{1+\tan^2 x}\)
31o lim\(\large \frac {4^x\:-\:\left(\frac 12\right)^x} {x} \) 32o lim\(\large \left( \frac {\ln x} {x}+ \frac{x}{e^x} \right)\)
33o lim\(\large \frac {x^x} {(x\,-\,1)^x} \) 34o lim\(\large \frac {1\,-\:\cos x} {1\,-\,x\,-\,e^{-x}} \)
35o lim\(\log_x 2 \) 36o lim\(\log_{\frac 12} x\)
37o lim\(\large x^{-\frac 2x} \) 38o lim\(\large \frac {e^2.\,x^2} {e^x} \)
39o lim\(\large \frac {e^x\,-\,1} {ex\,-\,1} \) 40o lim\(\large \frac {2^{x+2}-16} {4^x\,-\,16} \)
41o lim\(\ln\,(\tan x)\) 42o lim\(\;(\tan 2x.\ln \tan x)\)
43o lim\(\large \frac {\log x} {x\,-\,1} \) 44o lim\(\large \frac {\log_4 x} {\log_8 x} \)
45o lim\(\large \frac {\sqrt x} {\ln x} \) 46o lim\(\large \frac {e^{2+h}-\,e^2} {h} \)
47o lim\(\log_{0,3} \,e^x \) 48o lim\(\large \frac {\log_2\, (1\,-\,x^2)} {\log_4\, (\cos x)} \)

49o lim\( \left ( \frac{\sin {2x}}{ \sin x}+\frac{\log\; \sin {2x}}{\log\; \sin x} \right )\) nieuw
50o  (sin 1)x (tan 1)x e−x
51olim\(\large \frac {\ln(1\,+\,2x^2\,+\,4x^4)} {\ln(1\,+\,3x^4\,+\,9x^8)} \)
60r lim\(\large \frac{x^x}{(x\,+\,1)^x} \)
61r lim\(\large (\ln x)^{\frac {1} {x-e}} \)
62r lim\((\cos x)^{\frac {1} {\sin^{{\small 2}} x}} \)
63r lim\((\sin x + \cos x)^{\frac {1} {2x}} \)
64r lim\(\large \left( \frac {\tan x} {x} \right)^{\frac {1}{x^{\small 2}}} \)
65r lim\(\large \frac {(1\,+\,x)^{\frac 1x}\,-\,e} {x} \)
66r lim\(\left( e^{\frac 1x} + \frac 1x \right)^x \)
67r lim\(\large \left( \frac{\sin x}{x} \right) ^{\frac {1} {x^{\small 2}}} \)
68r lim\(\large \frac {\ln\,(1\,-\,x^2)} {\ln \cos x} \)
69r lim\(\large \left( \frac {x\,-\,2} {x\,-\,1} \right)^{x-1} \)
70r lim\(\large \left(\frac {3^x\,+\:4^x} {2}\right)^\frac 1x \)
71r lim\(\large \left(\frac {1\,+\,2x} {1\,+\,x}\right)^\frac{x-1}{x} \)
72r lim\( \left(1+2+3\,+\,...+\,n\right )^\frac 1n \)
73r lim\(\large \left ( x^2-x \right )^{\frac 2x}\)
74r lim\(\large \frac{e^x\:-\;x\;-\:1}{x^2}\) 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 16 aug 2024 ←