## 2019年6月20日木曜日

### 数学 - Python - 解析学 - 級数 - テイラーの公式 - 対数関数、三角関数(正接)、極限

1. $\begin{array}{l}\mathrm{log}\left(1+x\right)\\ =x-\frac{{x}^{2}}{2}+\frac{{x}^{3}}{3}-\dots \\ \mathrm{log}\left(1-x\right)\\ =-x-\frac{{x}^{2}}{2}-\frac{{x}^{3}}{3}-\dots \\ \mathrm{sin}x=x-\frac{1}{3!}{x}^{3}+\dots \\ \underset{x\to 0}{\mathrm{lim}}\frac{\mathrm{log}\left(1-x\right)}{\mathrm{sin}x}=-1\end{array}$

コード

Python 3

#!/usr/bin/env python3
from sympy import pprint, symbols, plot, Limit, sin, log

print('23.')

x = symbols('x')
f = log(1 - x) / sin(x)

for dir in ['+', '-']:
l = Limit(f, x, 0, dir=dir)
for o in [l, l.doit()]:
pprint(o)
print()

p = plot(log(1 - x), sin(x), f,
(x, -5, 5),
ylim=(-5, 5),
legend=True,
show=False)
colors = ['red', 'green', 'blue', 'brown', 'orange',
'purple', 'pink', 'gray', 'skyblue', 'yellow']

for o, color in zip(p, colors):
o.line_color = color

# p.show()
p.save('sample23.png')


C:\Users\...>py sample23.py
23.
⎛log(1 - x)⎞
lim ⎜──────────⎟
x─→0⁺⎝  sin(x)  ⎠

-1

⎛log(1 - x)⎞
lim ⎜──────────⎟
x─→0⁻⎝  sin(x)  ⎠

-1

C:\Users\...>