L I M I E T E N met goniom. getallen
  L I M I T S   ( involving sin x, cos x, tan x, ... ) recht
10 \(\cos x\) 11 \((\frac {x} {\sin x}\!+\!\frac {x} {\cos x}\!+\!\frac {x} {\tan x}) \)
12 \(\large \frac{\cos x}{x}\) 13 \(\large \frac {1-\sin x} {\cos^2 x} \; \)
14 \(\large \frac {\sin ax}{\sin bx}\) 15 \(\large \frac {\sin 4x \,\cdot\, \cos 2x} {\tan x} \)
16 \(\large \frac {\tan x}{4x}\) 17 \(\large \frac {\sin^2 x} {1-\,\cos x} \)
18 \(\large \frac {\sin^2 2x}{x^2}\) 19 \(\large \frac {\cos\,(\frac{\pi}{2}-x)} {x} \)
20 \(Bgtan\;x \) 21 \(\large \frac {1\,+\;\tan x} {\sin x} \)
30 \(\large\frac {\cot x} {x} \) 31 \(\large\frac{1\,-\,\tan x}{\sin x\,-\,\cos x} \) new
32 \( \cot x \) 33 \(\cos x \)  (ook x→)
34 \( {x\!\cdot\!\cot \frac x2} {} \) 35 \(\large \frac {\tan 6x} {\sin 2x \cdot \cos 3x} \)
36 \(\large \frac {\cos x\,-\,-x} {|x|} \) 37 \(\large \frac {\cos 2x - \cos x} {\sin^2 x} \)
38 \(\large \frac {\sin 2x} {\cos 3x} \) 39 \( \sin 2x \cdot \tan 3x \)
40 \(\large \frac {\cot 2x} {\cot x} \) 41 \(\large \frac {\sin^2 x\,+\,\tan^2 3x} {x^2} \)
42 \(2x \cdot \cot 2x \) 30 \(\large \frac {x+\sin 2x + \tan 3x} {x - \tan 2x} \)
43 \(\large \frac {\cos x - \cos a} {x\,-\,a} \) 44 \(\large \frac {\cos 2x - \cos 2a} {\cos x - \cos a} \)
45 \(\large \frac {\sin x - \sin 1} {x\,-\,1} \) 30 \(\large \frac {\sin x - \sin a} {x\,-\,a} \)
46 \(\large \frac {\sin x - \sin 4} {(x\,-\,4)^2} \) 47 \(\large \frac {\sin x - \sin \pi} {x\,-\,\pi} \)
48 \(\large \frac {x - \frac {\pi}{2}} {\cos x} \) 49 \(\large 64^{\frac {sin^2 x} {\tan 2x}} \)
50 \(\large \frac {\sin^2 3x} {5x} \) 51 \(\large \frac {\sin^5 2x} {4x^5} \)
52 \(\large \frac {\sin x^{\circ}} {x} \) 53 \(wait \)
54 \(\large \frac {2x - \pi} {\cot x} \) 55 \(\large \frac {x\,-\,\pi} {\sin x} \)
56 \(\large \frac {x\,+\,\sin 2x} {x\,-\,\tan 2x} \) 57 \(\large \frac {x\,-\,\tan x} {x\,-\,\sin x} \)
58 \(\large \frac {x\,-\,\sin 2x} {x\,-\,\sin 3x} \) 59 \(\large \frac {x\,+\,\sin 2x} {x\,+\,\sin x} \)
60 \(\large \frac {\tan x\,-\,\tan x} {x\:-\:a} \) 61 \(\large \frac {1\,-\,\cos 4x} {\cos 2x \,-\,1} \)
62 \(\large \frac {\large 1\,-\,\cos 2x} {1\,-\,\cos x} \) 63 \(\large \frac {\cos 16x\,-\,1} {1\,-\cos 4x} \)
64 \(\large \frac {1\:-\:\cos x} {x^2} \) 65 \(\large \frac {\cos ax\:-\:1} {x^2} \)
66 \(\large \frac {x\,\cdot\,\sin x} {1\:-\:\cos x} \) 67 \(\large \frac {x\:+\:\tan x} {1\,+\,x\,-\,\cos x} \)
68 \(\large \frac {\sin \frac{\pi}{3}\,-\,\sin x} {\cos\frac{\pi}{3}\,-\,\cos x} \) 69 \(\large \frac {\cos x} {\pi\:-\:2x} \)
70 \(\large \frac {2x} {\sin x\:-\:x} \) 71 \(\large \frac {\sin^2x\,+\,1\,-\,\cos x} {x^2} \)
72 \(\large \frac {x\,\cdot\,\sin 2x} {1\,-\,\cos 3x} \) 73 \(\large \frac {\cos x\:-\:1} {x} \)
74 \(\large \frac {\tan \pi x} {1\:-\:x} \) 75 \(\large \frac {\sin^2 5x\,\cdot\,\cos 3x} {\tan^22x} \)
76 \(\large \left (\!\!\frac{\left | x \right |}{\sin x}\!+\!\frac{\left | x \right|\!}{\cos x}\!\! \right )\) 77 \(\large \frac {\cos \frac 1x \,-\,1} {\frac {1}{x^2}} \)
78 \( (x\cdot\cos x\cdot\cot x\,)\) 79 \((x^2.\csc 2x.\cot 2x) \)
80 \( Bgtan\;x \) 81 \(\ln \tan x \)
82 \(Bgtan \:e^x \) 83 \(Bgtan \:e^x \)
84 \(\large f(x)\;=\;1\) 85 \((\cot x . Bgsin\:x)\)
86 limiet \( Correct\:?\;(1) \) 87 limiet   \(Correct\:? \;(2) \)
88 \(\large \frac {x^2} {1\:-\:\sec 2x} \) 89 \(\large \frac{4x.\sin^23x}{\cos5x.\tan^32x}\)
90 \(\large \frac {1-\,\cos x\,+\, x^2}{1\:-\:\cos x} \) 91 \(\large \frac {3.Bgtan \:x\,-\:x}{2x\,-\,Bgsin \:x} \)
92 \(\large \frac {1\,+\:\sin x}{\cos^2x}\) 93 \(\large \frac {1\,-\,\sqrt{1\,-\,\sin x}} {x} \)
94 \(\large \frac {\cos^3\!x\,-\,1} {x^2.\,\cos^2x} \)new 95 \((\frac {x} {\sin x}\!+\!\frac {x} {\cos x}\!+ \!\frac {x} {\tan x}\!+\!\frac {x} {\cot x}) \)
94 \(\large \frac {\ln x - \ln \sin x} {x^2} \) new 95 \((1-x).\tan\frac{\pi x}{2}\)
A0 \(\large \frac {\tan \,3x} {\tan \,5x} \) A1 \(\large \frac {\cos 3x} {\cos x} \) (2 limieten)
A2 \(\large \frac {1\,-\,\cos 2x} {1\:-\:\frac{\sin x}{x}} \) A3 \(\large \frac {1-\,\cos 2x.\cos x} {1\:-\:\cos x} \)
A4 \(\large \frac {1\,-\,\cos 3x} {1\:-\:\frac{\sin x}{x}} \) A5 \(\large \frac {\tan x \: - \: \sin x} {x^3} \)
A6 \((\cot \,x)^x\) A7 \((\sin 3x.\cos x.\tan 3x) \)
A8 \(\large \frac {1\,-\,\cos 4x} {\tan^2 3x} \) A9 \(\left ( \sin \frac{\pi}{3} - \sin x \right).\tan \frac{3x}{2} \)
B0 \(\large \frac {x\:+\:\sin 2x} {x^2\,+\:\tan x} \) B1 \(\large \frac {Bgcos\:x} {\sqrt{2\,-\,2x}} \)
B2 \(\large \frac {\sin x\:-\:\tan x} {\sin x\:-\:x} \) B3 \( \left ( \frac{1\,-\,\cos 3x}{1-\,\cos x} -\frac{1-\,\cos 2x}{1-\,\cos x} \right ) \)
B4 \(\large \frac {x\,-\,x\cos x} {x\,-\,\sin x} \) B5 \(\large \frac {1-\cos 2x} {x^2} vs. \frac{1-\cos x}{x^2} \)
B6 \(\large \frac {\cos \frac1x -1} {\frac{1}{x^2}} \) B7 \(\large \frac {x} {D\frac{x}{\sin x}} \)
B8 \(\large \frac {x\,-\,Bgtan\:x} {x\,-\,\sin x} \) B9 \(\large \frac {2\sin x - \sin 2x} {x\:-\:\sin x} \)
C0 \(\large \frac {x\:-\sin x} {x^3} \) C1 \(\large (\cos x)^{\frac{1}{x^2}} \)
C2 \(\large \frac {\sin (x-\frac{\pi}{3})} {1-2.\cos x} \) C3 \(\large (\frac {\sin x} {x})^{\frac{1}{x^2}} \)
C2 \(\large \frac {\sin x\,+\,\cos 2x} {1\,-\,\sin x} \) C4 \(\left [ (x-1).\tan \frac{\pi x}{2} \right ] \)
C4 \((\tan \alpha)^x= \) C5 \(\large \frac {(3x\,-\,1)^8-\,(x\,-\,1)^8} {\sin x} \)
C6 \(\large \frac {\ln\:(1\,-\,x^2)} {\ln \cos x} \) C7 \(\large f(x) = \large \frac {1}{1-\sin x-\cos x} \)
C8 \(\large \frac {\tan x} {x^n}\small ∈\) new C9 \(\large \frac{1-\,\cos x\,+\,x.\sin x}{2x^2} \) new

D0 voor welke f is lim f (x)=
D1 \(\small \displaystyle \lim_{n \to +\infty} \left [4^n.\left ( 1-\cos \frac{1}{2^n} \right ) \right ]\)
D1 \(\displaystyle \lim_{x \to 0}\: \left ( \frac{\tan x}{x} \right )^{\frac{1}{x^2}}\)

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)

limits of polynomial fractions (a)

limieten van veeltermbreuken (b)

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





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vanaf 1 jan. 2021