ЛР6

Пример 1

import sympy as sp from sympy.abc import x sp.plot(sp.cos(x),(x,0,2*sp.pi)) y = sp.cos(x) sp.plot(y,(x,0,2*sp.pi)) sp.plot(y,(x,0,2*sp.pi),adaptive=False,nb_of_points=10,line_color='r')

<sympy.plotting.plot.Plot at 0x66e5b90>

import sympy as sp from sympy.abc import x y = sp.sin(x)/(x**2+1) sp.plot(sp.sin(x)/(x**2+1),(x,-20,20)) sp.plot(y,(x,-20,20))

<sympy.plotting.plot.Plot at 0x663ee18>

Пример 2

import sympy as sp from matplotlib import style from sympy.abc import x style.use('ggplot') y = sp.Abs(x)/x sp.plot((y,(x,-1,0)),(y,(x,0,1))) sp.plot(y,(x,-1,1))

<sympy.plotting.plot.Plot at 0x73689a8>

Упражнение 1

from sympy.abc import x import matplotlib.pyplot as plt plt.axis('equal') y1=(2*x-1)/(x-1) y2=(2*x-1)/sp.Abs(x-1) sp.plot((y1,(x,0,1)),(y1,(x,1,2)),adaptive=False, nb_of_points=10) sp.plot(y2,(x,0,2),adaptive=False, nb_of_points=20)

<sympy.plotting.plot.Plot at 0x1589dea8>

Пример 3

import sympy as sp from sympy.abc import x y = sp.sin(x)/x sp.plot(y)

<sympy.plotting.plot.Plot at 0xe360a60>

Упражнение 2

from sympy.abc import x y1=(1+x)**(1/x) y2=((sp.sin(x**2/sp.sqrt(1-x**3)))/(x*sp.log(1-x**3))) sp.plot(y1,(x,-2,2),adaptive=False, nb_of_points=70) sp.plot(y2,(x,-2,2),adaptive=False, nb_of_points=40)

<sympy.plotting.plot.Plot at 0x15f1e010>

а)1 ; б)-оо

Пример 4

import sympy as sp from sympy.abc import x, a sp.limit((1+a/x)**x,x,sp.oo)

exp(a)

import sympy as sp from sympy.abc import x sp.limit(1/x**3,x,0,'-')

-oo

Пример 5

import sympy as sp from sympy.abc import x sp.limit(sp.sin(x),x,sp.oo)

AccumBounds(-1, 1)

Упражнение 3

import sympy as sp from sympy.abc import x sp.limit((1+x)**(1/x),x,sp.oo,'+')

1

import sympy as sp from sympy.abc import x sp.limit(((sp.sin(x**2/sp.sqrt(1-x**3)))/(x*sp.log(1-x**3))),x,0)

-oo

Упражнение С1

from sympy.abc import x y1=sp.Abs((2*x-1)/(x-1)) y2=(sp.Abs(3*x-6))/(x-2) sp.plot(y1,(x,-2,5),adaptive=False, nb_of_points=40) sp.plot((y2,(x,-1,2)),(y2,(x,2,5)))

<sympy.plotting.plot.Plot at 0x15138758>

Упражнение С2

from sympy.abc import x import numpy as np import matplotlib.pyplot as plt y1=sp.log(x)*sp.sin(x) y2=(2**x)/(sp.factorial(x)) sp.plot(y1) sp.plot(y2,(x,0,100))

<sympy.plotting.plot.Plot at 0x7c438b8>

Упражнение С3

import sympy as sp from sympy.abc import x sp.limit(sp.log(x)*sp.sin(x),x,sp.oo)

AccumBounds(-oo, oo)

import sympy as sp from sympy.abc import x sp.limit((2**x)/(sp.factorial(x)),x,sp.oo)

0