Python人工智能数学基础-微积分

求极限lim（x→∞）sinx/x

import sympy
from sympy import oo # 注意无穷符号表示形式为两个小写字母 o
x=sympy.Symbol('x') # 注意 Symbol 第一字母大写
f=sympy.sin(x)/x
print (sympy.limit(f,x,oo))

求极限lim（x→∞）sinx/(3x+x³)

import sympy
x=sympy.Symbol('x') 
f=sympy.sin(x)/(3*x+x**3)
print(sympy.limit(f,x,0))

求导数y=arcsin√(sinx)

from sympy import * 
from sympy.abc import x,y,z,f
print(diff(asin(sqrt(sin(x)))))

求f(x,y)=x²+3xy+y²在(1,2)初的偏导数

from sympy import * 
from sympy.abc import x,y,z,f
f=x**2+3*x*y+y**2
print(diff(f,x)) # 求偏导
print(diff(f,y))
fx=diff(f,x) # 求偏导并将结果赋给 fx
print(fx.evalf(subs={
    
    x:1,y:2}))# 以字典的形式传入多个变量的值，求函数值。
fy=diff(f,y)
print(fy.evalf(subs={
    
    x:1,y:2}))

求定积分∫(0,3) cos²(e^x)

import numpy as np 
from scipy.integrate import quad
f=lambda x:np.cos(np.exp(x))**2 # 定义被积分函数
solution=quad(f,0,3) # 调用 quad 积分函数
print(solution)

求二重积分∬(0≤x≤10, 0≤y≤10) e^(-x²-y²)dxdy

import numpy as np
from scipy.integrate import dblquad
def integrand(x,y):
  return np.exp(-x**2-y**2)
x_a=0
x_b=10
y_a=0
y_b=10
solution,abserr=dblquad(integrand, x_a, x_b, lambda x:y_a, lambda x:y_b)
print(solution,abserr)