视频讲解地址https://www.bilibili.com/video/BV12V4y1w7Rs/

所用语句如下：

import sympy as smp
from sympy import *

x,y = smp.symbols("x y")

f = x**12 + y

f.subs(x,4)

g = smp.asin(x)

g.subs(x,1)

g1 = smp.tan(x)

g1.subs(x,1)

smp.log(81,9)

x**(9/2)

求极限

smp.sin(x/2 + smp.sin(x))

smp.limit(smp.sin(x/2 + smp.sin(x)),x,smp.pi)

2*smp.exp(1/x) / (smp.exp(1/x)+1)

smp.limit(2*smp.exp(1/x) / (smp.exp(1/x)+1),x,0,dir='+')

smp.limit((smp.cos(x)-1)/x,x,smp.oo)

(smp.cos(x)-1)/x

((1+smp.sin(x))/(1-smp.cos(x)))**2

smp.diff( ((1+smp.sin(x))/(1-smp.cos(x)))**2,x)

smp.diff( ((y+smp.sin(x))/(1-smp.cos(x)))**2,x)

smp.log(x,5)**(x/2)

smp.diff((smp.log(x,5)**(x/2)),x)

f,g,p = smp.symbols('f g p',cls=smp.Function)

g = g(x)
f = f(x+g)

smp.diff(f,x)

p = p(x**2+f)

smp.diff(p,x)

smp.integrate(smp.csc(x)*smp.cot(x),x)

// 默认不加C

smp.integrate(4*smp.sec(3*x)*smp.tan(3*x),x)

2/smp.sqrt(1-x**2) - 1/x**(1/4)
smp.integrate(2/smp.sqrt(1-x**2) - 1/x**(1/4),x)

2/smp.sqrt(1-x**2) - 1/x**smp.Rational(1,4)
smp.integrate(2/smp.sqrt(1-x**2) - 1/x**smp.Rational(1,4),x)

f1=x+y-3
f2=x-y+5
solve([f1,f2],[x,y])

f1=sin(x)/x
f2=(1+x)**(1/x)
f3=(1+1/x)**x
lim1=limit(f1,x,0)
lim2=limit(f2,x,0)
lim3=limit(f3,x,oo)
print(lim1,lim2,lim3)

(1+smp.sqrt(x))**smp.Rational(1,3)/smp.sqrt(x)
smp.integrate((1+smp.sqrt(x))**smp.Rational(1,3)/smp.sqrt(x),x)
x*(1-x**2)**smp.Rational(1,4)
smp.integrate(x*(1-x**2)**smp.Rational(1,4),x)
(2*x-1)*cos((3*(2*x-1)**2+6)**smp.Rational(1,2))/(3*(2*x-1)**2+6)**smp.Rational(1,2)
smp.integrate((2*x-1)*cos((3*(2*x-1)**2+6)**smp.Rational(1,2))/(3*(2*x-1)**2+6)**smp.Rational(1,2),x)
smp.integrate(smp.exp(x)/smp.sqrt(smp.exp(2*x)+9),(x,0,smp.log(4)))
t = smp.symbols('t')
smp.integrate(x**10*smp.exp(x),(x,1,t))
(16*atan(x))/(1+x**2)
smp.integrate((16*atan(x))/(1+x**2),(x,0,oo))
n=smp.symbols('n')
smp.Sum(6/4**n,(n,0,smp.oo))
smp.Sum(6/4**n,(n,0,smp.oo)).doit()

smp.Sum(smp.atan(n)/n**smp.Rational(11,10),(n,1,smp.oo)).n()
smp.Sum((1+smp.cos(n))/n**2,(n,1,smp.oo)).n()