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

LIMITS (involving log or Euler's number (e)
10g lim\(\left ( 1-h \right )^\frac1h\) 11g Limiet is  -o new
12g lim\(\left ( 1+\frac 1x \right )^{x+3} \) 13g \(\frac {n\,+\,1} {n} \) en \( \left(\frac {n\,+\,1} {n}\right)^n \)
14g lim\(\sqrt[x]{x+1}\) 15g lim\(\,\log_3\,(x+1)^2 \)
16g lim\(\log \,(2x) \) 17g lim\(\left( \frac e3 \right)^x\)
18o \(\frac{n+1}{n}\) als n → +oneindig 19g lim\(\frac{e^{-x}+\,x\,-\,2}{x^2}\) new
20o lim\(\left ( \frac{x\,+\,6}{x} \right )^{3x} \) 21o lim\(\sqrt[x]{x}\)
22o lim\(\left ( \frac{1\,+\,x}{x} \right )^{4-3x}\) **o lim\(\left(1+\frac1x\right)^x\) new
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\(\large\frac{\log x}{\cot x}\) new 50olim\(\large \frac {\ln(1\,+\,2x^2\,+\,4x^4)} {\ln(1\,+\,3x^4\,+\,9x^8)} \)
51o lim\((\cos x)^\frac{1}{x^2}\)new 52r lim\((\cos x)^{\frac {1} {\sin^{{\small 2}} x}} \)

53o lim\( \left ( \frac{\sin {2x}}{ \sin x}+\frac{\log\; \sin {2x}}{\log\; \sin x} \right )\) nieuw
54o  (sin 1)x (tan 1)x e−x
60r lim\(\large \frac{x^x}{(x\,+\,1)^x} \)
61r lim\(\large (\ln x)^{\frac {1} {x-e}} \)
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
75r lim\(\left[(2x+3)\cdot\ln\frac{x\,-\,1}{x\,-\,4}\right]\) nieuw
76r lim\(\left(\frac{x\,-\,1}{x\,-\,4}\right)^{2x+3}\) nieuw
77r lim\(\large\left(\frac{\sin x}{x}\right)^{\frac{1}{1\,-\;\cos x}}\) nieuw
78r lim\(\left(\frac{x-1}{x-4}\right)^{2x+3}\)
79r lim\(\left[(2x+3)\cdot\ln\frac{x-1}{x-4}\right]\)
80r lim\(\large\frac{\ln\frac{x^2}{4}}{x^3-8}\) new
81r lim\(\left[\:x\left(1-\sqrt[x]{2}\right)\,\right]\) new
82r lim\(\large\frac{\ln(1\,+\,3x^2)\,-\,3x^2}{x^4}\) new



➔ 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 ←