De functie f (x) = ax − xa


- Grafieken van de functie
- Tabel 1: De nulpunten van de functie voor a = 0 tot en met a = 10 in stappen van 0.001 met twintig cijfers achter de komma

De grafiek van f (x) voor a = 0.00 (de rode lijn),
a = 0.05 (de lichtgroene lijn), a = 0.10 (de oranje lijn),
a = 0.20 (de paarse lijn), a = 0.30 (de donkerblauwe lijn),
a = 0.40 (de grijze lijn), a = 0.50 (de donkerbruine lijn),
a = 0.60 (de lichtbruine lijn), a = 0.70 (de donkergroene lijn),
a = 0.80 (de gele lijn), a = 0.90 (de lichtblauwe lijn)
en a = 1.00 (de violet lijn)

De grafiek van f (x) voor a = 1.0 (de rode lijn),
a = 1.1 (de lichtgroene lijn), a = 1.2 (de oranje lijn),
a = 1.3 (de paarse lijn), a = 1.4 (de donkerblauwe lijn),
a = 1.5 (de grijze lijn), a = 1.6 (de donkerbruine lijn),
a = 1.7 (de lichtbruine lijn), a = 1.8 (de donkergroene lijn),
a = 1.9 (de gele lijn) en a = 2.0 (de lichtblauwe lijn)

De grafiek van f (x) voor a = 2.0 (de rode lijn),
a = 2.1 (de lichtgroene lijn), a = 2.2 (de oranje lijn),
a = 2.3 (de paarse lijn), a = 2.4 (de donkerblauwe lijn),
a = 2.5 (de grijze lijn), a = 2.6 (de donkerbruine lijn),
a = 2.7 (de lichtbruine lijn), a = 2.8 (de donkergroene lijn),
a = 2.9 (de gele lijn) en a = 3.0 (de lichtblauwe lijn)

De grafiek van f (x) voor a = 3.0 (de rode lijn),
a = 3.1 (de lichtgroene lijn), a = 3.2 (de oranje lijn),
a = 3.3 (de paarse lijn), a = 3.4 (de donkerblauwe lijn),
a = 3.5 (de grijze lijn), a = 3.6 (de donkerbruine lijn),
a = 3.7 (de lichtbruine lijn), a = 3.8 (de donkergroene lijn),
a = 3.9 (de gele lijn) en a = 4.0 (de lichtblauwe lijn)

De grafiek van f (x) voor a = e − 0.5 (de rode lijn),
a = e − 0.4 (de lichtgroene lijn), a = e − 0.3 (de oranje lijn),
a = e − 0.2 (de paarse lijn), a = e − 0.1 (de donkerblauwe lijn),
a = e (de grijze lijn), a = e + 0.1 (de donkerbruine lijn),
a = e + 0.2 (de lichtbruine lijn), a = e + 0.3 (de donkergroene lijn),
a = e + 0.4 (de gele lijn) en a = e + 0.5 (de lichtblauwe lijn)

De grafiek van de nulpunten van f (x):
n1 (de rode lijn) en n2 (de groene lijn)
a | n1 | n2 |
0.000 | ||
0.001 | 0.00100000000000000000 | |
0.002 | 0.00200000000000000000 | |
0.003 | 0.00300000000000000000 | |
0.004 | 0.00400000000000000000 | |
0.005 | 0.00500000000000000000 | |
0.006 | 0.00600000000000000000 | |
0.007 | 0.00700000000000000000 | |
0.008 | 0.00800000000000000000 | |
0.009 | 0.00900000000000000000 | |
0.010 | 0.01000000000000000000 | |
0.011 | 0.01100000000000000000 | |
0.012 | 0.01200000000000000000 | |
0.013 | 0.01300000000000000000 | |
0.014 | 0.01400000000000000000 | |
0.015 | 0.01500000000000000000 | |
0.016 | 0.01600000000000000000 | |
0.017 | 0.01700000000000000000 | |
0.018 | 0.01800000000000000000 | |
0.019 | 0.01900000000000000000 | |
0.020 | 0.02000000000000000000 | |
0.021 | 0.02100000000000000000 | |
0.022 | 0.02200000000000000000 | |
0.023 | 0.02300000000000000000 | |
0.024 | 0.02400000000000000000 | |
0.025 | 0.02500000000000000000 | |
0.026 | 0.02600000000000000000 | |
0.027 | 0.02700000000000000000 | |
0.028 | 0.02800000000000000000 | |
0.029 | 0.02900000000000000000 | |
0.030 | 0.03000000000000000000 | |
0.031 | 0.03100000000000000000 | |
0.032 | 0.03200000000000000000 | |
0.033 | 0.03300000000000000000 | |
0.034 | 0.03400000000000000000 | |
0.035 | 0.03500000000000000000 | |
0.036 | 0.03600000000000000000 | |
0.037 | 0.03700000000000000000 | |
0.038 | 0.03800000000000000000 | |
0.039 | 0.03900000000000000000 | |
0.040 | 0.04000000000000000000 | |
0.041 | 0.04100000000000000000 | |
0.042 | 0.04200000000000000000 | |
0.043 | 0.04300000000000000000 | |
0.044 | 0.04400000000000000000 | |
0.045 | 0.04500000000000000000 | |
0.046 | 0.04600000000000000000 | |
0.047 | 0.04700000000000000000 | |
0.048 | 0.04800000000000000000 | |
0.049 | 0.04900000000000000000 | |
0.050 | 0.05000000000000000000 | |
0.051 | 0.05100000000000000000 | |
0.052 | 0.05200000000000000000 | |
0.053 | 0.05300000000000000000 | |
0.054 | 0.05400000000000000000 | |
0.055 | 0.05500000000000000000 | |
0.056 | 0.05600000000000000000 | |
0.057 | 0.05700000000000000000 | |
0.058 | 0.05800000000000000000 | |
0.059 | 0.05900000000000000000 | |
0.060 | 0.06000000000000000000 | |
0.061 | 0.06100000000000000000 | |
0.062 | 0.06200000000000000000 | |
0.063 | 0.06300000000000000000 | |
0.064 | 0.06400000000000000000 | |
0.065 | 0.06500000000000000000 | |
0.066 | 0.06600000000000000000 | |
0.067 | 0.06700000000000000000 | |
0.068 | 0.06800000000000000000 | |
0.069 | 0.06900000000000000000 | |
0.070 | 0.07000000000000000000 | |
0.071 | 0.07100000000000000000 | |
0.072 | 0.07200000000000000000 | |
0.073 | 0.07300000000000000000 | |
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0.075 | 0.07500000000000000000 | |
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0.080 | 0.08000000000000000000 | |
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0.100 | 0.10000000000000000000 | |
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0.103 | 0.10300000000000000000 | |
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