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01 |
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\(\cos x\) |
02 |
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\((\frac {x} {\sin x}\!+\!\frac {x} {\cos x}\!+\!\frac {x} {\tan x}) \) |
| 03 |
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\(\large \frac{\cos x}{x}\) |
04 |
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\(\large \frac {1-\sin x} {\cos^2 x} \; \) |
| 05 |
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\(\large \frac {\sin ax}{\sin bx}\) |
06 |
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\(\large \frac {\sin 4x \,\cdot\, \cos 2x} {\tan x} \) |
| 07 |
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\(\large \frac {\tan x}{4x}\) |
08 |
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\(\large \frac {\sin^2 x} {1-\,\cos x} \) |
| 09 |
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\(\large \frac {\sin^2 2x}{x^2}\) |
10 |
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\(\large \frac {\cos\,(\frac{\pi}{2}-x)} {x} \) |
| 11 |
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\(\large \frac{x}{\sin x\,+\,\tan x}\) |
12 |
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\(\left[x^2\cdot{\sin\frac{1}{x^2}}\right]\) |
| 13 |
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\(Bgtan\;x \) |
14 |
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\(\large \frac {1\,+\;\tan x} {\sin x} \) |
20 |
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\(\large\frac {\cot x} {x} \) |
21 |
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\(\large\frac{1\,-\,\tan x}{\sin x\,-\,\cos x} \) |
| 22 |
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\( \cot x \) |
23 |
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\(\cos x \) (ook x→ ) |
| 24 |
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\( {x\!\cdot\!\cot \frac x2} {} \) |
25 |
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\(\large \frac {\tan 6x} {\sin 2x \cdot \cos 3x} \) |
| 26 |
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\(\large \frac {\cos x\,-\,-x} {|x|} \) |
27 |
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\(\large \frac {\cos 2x - \cos x} {\sin^2 x} \) |
| 28 |
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\(\large \frac {\sin 2x} {\cos 3x} \) |
29 |
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\( \sin 2x \cdot \tan 3x \) |
| 30 |
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\(\large \frac {\cot 2x} {\cot x} \) |
31 |
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\(\large \frac {\sin^2 x\,+\,\tan^2 3x} {x^2} \) |
| 32 |
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\(2x \cdot \cot 2x \) |
33 |
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\(\large \frac {x+\sin 2x + \tan 3x} {x - \tan 2x} \) |
| 34 |
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\(\large \frac {\cos x - \cos a} {x\,-\,a} \) |
35 |
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\(\large \frac {\cos 2x - \cos 2a} {\cos x - \cos a} \) |
| 36 |
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\(\large \frac {\sin x - \sin 1} {x\,-\,1} \) |
37 |
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\(\large \frac {\sin x - \sin a} {x\,-\,a} \) |
| 38 |
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\(\large \frac {\sin x - \sin 4} {(x\,-\,4)^2} \) |
39 |
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\(\large \frac {\sin x - \sin \pi} {x\,-\,\pi} \) |
| 40 |
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\(\large \frac {x - \frac {\pi}{2}} {\cos x} \) |
41 |
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\(\large 64^{\frac {sin^2 x} {\tan 2x}} \) |
| 42 |
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\(\large \frac {\sin^2 3x} {5x} \) |
43 |
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\(\large \frac {\sin^5 2x} {4x^5} \) |
| 44 |
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\(\large \frac {\sin x^{\circ}} {x} \) |
45 |
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\(wait \) |
| 46 |
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\(\large \frac {2x - \pi} {\cot x} \) |
47 |
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\(\large \frac {x\,-\,\pi} {\sin x} \) |
| 48 |
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\(\large \frac {x\,+\,\sin 2x} {x\,-\,\tan 2x} \) |
49 |
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\(\large \frac {x\,-\,\tan x} {x\,-\,\sin x} \) |
| 50 |
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\(\large \frac {x\,-\,\sin 2x} {x\,-\,\sin 3x} \) |
51 |
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\(\large \frac {x\,+\,\sin 2x} {x\,+\,\sin x} \) |
| 52 |
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\(\large \frac {\tan x\,-\,\tan x} {x\:-\:a} \) |
53 |
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\(\large \frac {1\,-\,\cos 4x} {\cos 2x \,-\,1} \) |
| 54 |
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\(\large \frac {\large 1\,-\,\cos 2x} {1\,-\,\cos x} \) |
55 |
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\(\large \frac {\cos 16x\,-\,1} {1\,-\cos 4x} \) |
| 56 |
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\(\large \frac {1\:-\:\cos x} {x^2} \) |
57 |
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\(\large \frac {\cos ax\:-\:1} {x^2} \) |
| 58 |
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\(\large \frac {x\,\cdot\,\sin x} {1\:-\:\cos x} \) |
59 |
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\(\large \frac {x\:+\:\tan x} {1\,+\,x\,-\,\cos x} \) |
| 60 |
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\(\large \frac {\sin \frac{\pi}{3}\,-\,\sin x} {\cos\frac{\pi}{3}\,-\,\cos x} \) |
61 |
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\(\large \frac {\cos x} {\pi\:-\:2x} \) |
| 62 |
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\(\large \frac {2x} {\sin x\:-\:x} \) |
63 |
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\(\large \frac {\sin^2x\,+\,1\,-\,\cos x} {x^2} \) |
| 64 |
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\(\large \frac {x\,\cdot\,\sin 2x} {1\,-\,\cos 3x} \) |
65 |
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\(\large \frac {\cos x\:-\:1} {x} \) |
| 66 |
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\(\large \frac {\tan \pi x} {1\:-\:x} \) |
67 |
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\(\large \frac {\sin^2 5x\,\cdot\,\cos 3x} {\tan^22x} \) |
| 68 |
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\(\left (\!\!\frac{\left | x \right |}{\sin x}\!\!+\!\!\frac{\left | x \right|\!}{\cos x}\!\! \right )\) |
69 |
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\(\large \frac {\cos \frac 1x \,-\,1} {\frac {1}{x^2}} \) |
| 70 |
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\(\small (x\!\cdot\!\cos x\!\cdot\!\cot x)\) |
71 |
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\((x^2.\csc 2x.\cot 2x) \) |
| 72 |
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\( Bgtan\;x \) |
73 |
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\(\ln \tan x \) |
| 74 |
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\(Bgtan \:e^x \) |
75 |
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\(Bgtan \:e^x \) |
| 76 |
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\(\large f(x)\;=\;1\) |
77 |
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\((\cot x . Bgsin\:x)\) |
78 |
limiet |
\(\small Correct\:?\;(1) \) |
79 |
limiet |
\(\small Correct\:? \;(2) \) |
| 80 |
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\(\large \frac {x^2} {1\:-\:\sec 2x} \) |
81 |
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\(\large \frac{4x.\sin^23x}{\cos5x.\tan^32x}\) |
| 82 |
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\(\large \frac {1-\,\cos x\,+\, x^2}{1\:-\:\cos x} \) |
83 |
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\(\large \frac {3.Bgtan \:x\,-\:x}{2x\,-\,Bgsin \:x} \) |
| 84 |
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\(\large \frac {1\,+\:\sin x}{\cos^2x}\) |
85 |
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\(\large \frac {1\,-\,\sqrt{1\,-\,\sin x}} {x} \) |
| 86 |
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\(\large \frac {\cos^3\!x\,-\,1} {x^2.\,\cos^2x} \) |
87 |
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\((\small\frac {x} {\sin x}\!+\!\frac {x} {\cos x}\!+ \!\frac {x} {\tan x}\!+\!\frac {x} {\cot x}) \) |
| 88 |
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\(\large \frac {\ln x - \ln \sin x} {x^2} \) |
89 |
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\((1-x).\tan\frac{\pi x}{2}\) |
| 90 |
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\(\large\frac{\sin(x-1)}{x^2-1} \) |
91 |
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\(\small \left [ (4x^2\!-\!1).\cot(2x\!-\!1) \right ]\) |
| 92 |
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\(\large\frac{\log x}{\cot x}\) |
93 |
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\( 2x\sin\frac 4x\) |
| 94 |
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\(\frac{2\sin x}{x-|x|}\) |
95 |
lim |
L a t e r |
| A0 |
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\(\large \frac {\tan \,3x} {\tan \,5x} \) |
A1 |
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\(\large \frac {\cos 3x} {\cos x} \) (2 limieten) |
| A2 |
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\(\large \frac {1\,-\,\cos 2x} {1\:-\:\frac{\sin x}{x}} \) |
A3 |
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\(\large \frac {1-\,\cos 2x.\cos x} {1\:-\:\cos x} \) |
| A4 |
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\(\large \frac {1\,-\,\cos 3x} {1\:-\:\frac{\sin x}{x}} \) |
A5 |
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\(\large \frac {\tan x \: - \: \sin x} {x^3} \) |
| A6 |
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\((\cot \,x)^x\) |
A7 |
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\((\sin 3x.\cos x.\tan 3x) \) |
| A8 |
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\(\large \frac {1\,-\,\cos 4x} {\tan^2 3x} \) |
A9 |
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\(\left ( \sin \frac{\pi}{3} - \sin x \right).\tan \frac{3x}{2} \) |
| B0 |
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\(\large \frac {x\:+\:\sin 2x} {x^2\,+\:\tan x} \) |
B1 |
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\(\large \frac {Bgcos\:x} {\sqrt{2\,-\,2x}} \) |
| B2 |
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\(\large \frac {\sin x\:-\:\tan x} {\sin x\:-\:x} \) |
B3 |
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\( \left ( \frac{1\,-\,\cos 3x}{1-\,\cos x} -\frac{1-\,\cos 2x}{1-\,\cos x} \right ) \) |
| B4 |
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\(\large \frac {x\,-\,x\cos x} {x\,-\,\sin x} \) |
B5 |
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\(\large \frac {1-\cos 2x} {x^2} vs. \frac{1-\cos x}{x^2} \) |
| B6 |
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\(\large \frac {\cos \frac1x -1} {\frac{1}{x^2}} \) |
B7 |
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\(\large \frac {x} {D\frac{x}{\sin x}} \) |
| B8 |
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\(\large \frac {x\,-\,Bgtan\:x} {x\,-\,\sin x} \) |
B9 |
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\(\large \frac {2\sin x - \sin 2x} {x\:-\:\sin x} \) |
| C0 |
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\(\large \frac {x\:-\sin x} {x^3} \) |
C1 |
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\(\large (\cos x)^{\frac{1}{x^2}} \) |
| C2 |
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\(\large \frac {\sin (x-\frac{\pi}{3})} {1-2.\cos x} \) |
C3 |
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\(\large (\frac {\sin x} {x})^{\frac{1}{x^2}} \) |
| C2 |
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\(\large \frac {\sin x\,+\,\cos 2x} {1\,-\,\sin x} \) |
C4 |
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\(\left [ (x-1).\tan \frac{\pi x}{2} \right ] \) |
| C4 |
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\((\tan \alpha)^x\!= \) |
C5 |
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\(\large \frac {(3x\,-\,1)^8-\,(x\,-\,1)^8} {\sin x} \) |
| C6 |
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\(\large \frac {\ln\:(1\,-\,x^2)} {\ln \cos x} \) |
C7 |
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\(\small f(x) = \large \frac {1}{1-\sin x-\cos x} \) |
| C8 |
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\(\large \frac {\tan x} {x^n}\small ∈\;\) |
C9 |
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\(\large \frac{1-\,\cos x\,+\,x.\sin x}{2x^2} \) |
| D0 |
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\(\large\frac{\sin x}{1-\cos x}\) |
D1 |
| \(\large\frac{\cos 2x-1}{\cos x-1}\) |
| D2 |
| \(\large\frac{1-\cos x}{x\cdot\tan x}\) |
D3 |
| \(\large\frac{2-\cos x-\cos^2x}{x^2}\) |
| D4 |
| \(\large\frac{\sin^3x}{\sin x-\tan x}\) |
D5 |
| \(\large\frac{x^3+\sin^3x}{x^3}\) |
| D6 |
| \(\large\frac{x-\sin x}{x\,\cdot\,\sin^2x}\) |
D7 |
| \(\large\frac{x^3-\sin^3x}{x^5}\) |
| D8 |
| \(\large\frac{x^6-\tan^6x}{x^8}\) |
D9 |
| \(\large\frac{\sin^62x-x^6}{x^6}\) |
| D8 |
| \(\large\frac{x^4-\sin^4x}{x^6}\) |
D9 |
| \(\large\frac{x^6-\sin^6x}{x^8}\) |
| E0 |
| \(\large\frac{\cos x}{\cos 5x}\) |
E1 |
| \(\large\frac{x^3-\sin^3x}{\sin x^5}\) |