Skip to content
Permalink
Branch: master
Find file Copy path
Find file Copy path
8 contributors

Users who have contributed to this file

@certik @smichr @navytux @oscargus @skirpichev @mattpap @jrioux @thegedge
138 lines (97 sloc) 4.56 KB
from sympy import limit, Symbol, oo, sqrt, Rational, log, exp, cos, sin, tan, \
pi, asin, together, root, S
# Numbers listed with the tests refer to problem numbers in the book
# "Anti-demidovich, problemas resueltos, Ed. URSS"
x = Symbol("x")
def test_leadterm():
assert (3 + 2*x**(log(3)/log(2) - 1)).leadterm(x) == (3, 0)
def root3(x):
return root(x, 3)
def root4(x):
return root(x, 4)
def test_Limits_simple_0():
assert limit((2**(x + 1) + 3**(x + 1))/(2**x + 3**x), x, oo) == 3 # 175
def test_Limits_simple_1():
assert limit((x + 1)*(x + 2)*(x + 3)/x**3, x, oo) == 1 # 172
assert limit(sqrt(x + 1) - sqrt(x), x, oo) == 0 # 179
assert limit((2*x - 3)*(3*x + 5)*(4*x - 6)/(3*x**3 + x - 1), x, oo) == 8 # Primjer 1
assert limit(x/root3(x**3 + 10), x, oo) == 1 # Primjer 2
assert limit((x + 1)**2/(x**2 + 1), x, oo) == 1 # 181
def test_Limits_simple_2():
assert limit(1000*x/(x**2 - 1), x, oo) == 0 # 182
assert limit((x**2 - 5*x + 1)/(3*x + 7), x, oo) is oo # 183
assert limit((2*x**2 - x + 3)/(x**3 - 8*x + 5), x, oo) == 0 # 184
assert limit((2*x**2 - 3*x - 4)/sqrt(x**4 + 1), x, oo) == 2 # 186
assert limit((2*x + 3)/(x + root3(x)), x, oo) == 2 # 187
assert limit(x**2/(10 + x*sqrt(x)), x, oo) is oo # 188
assert limit(root3(x**2 + 1)/(x + 1), x, oo) == 0 # 189
assert limit(sqrt(x)/sqrt(x + sqrt(x + sqrt(x))), x, oo) == 1 # 190
def test_Limits_simple_3a():
a = Symbol('a')
#issue 3513
assert together(limit((x**2 - (a + 1)*x + a)/(x**3 - a**3), x, a)) == \
(a - 1)/(3*a**2) # 196
def test_Limits_simple_3b():
h = Symbol("h")
assert limit(((x + h)**3 - x**3)/h, h, 0) == 3*x**2 # 197
assert limit((1/(1 - x) - 3/(1 - x**3)), x, 1) == -1 # 198
assert limit((sqrt(1 + x) - 1)/(root3(1 + x) - 1), x, 0) == Rational(3)/2 # Primer 4
assert limit((sqrt(x) - 1)/(x - 1), x, 1) == Rational(1)/2 # 199
assert limit((sqrt(x) - 8)/(root3(x) - 4), x, 64) == 3 # 200
assert limit((root3(x) - 1)/(root4(x) - 1), x, 1) == Rational(4)/3 # 201
assert limit(
(root3(x**2) - 2*root3(x) + 1)/(x - 1)**2, x, 1) == Rational(1)/9 # 202
def test_Limits_simple_4a():
a = Symbol('a')
assert limit((sqrt(x) - sqrt(a))/(x - a), x, a) == 1/(2*sqrt(a)) # Primer 5
assert limit((sqrt(x) - 1)/(root3(x) - 1), x, 1) == Rational(3, 2) # 205
assert limit((sqrt(1 + x) - sqrt(1 - x))/x, x, 0) == 1 # 207
assert limit(sqrt(x**2 - 5*x + 6) - x, x, oo) == Rational(-5, 2) # 213
def test_limits_simple_4aa():
assert limit(x*(sqrt(x**2 + 1) - x), x, oo) == Rational(1)/2 # 214
def test_Limits_simple_4b():
#issue 3511
assert limit(x - root3(x**3 - 1), x, oo) == 0 # 215
def test_Limits_simple_4c():
assert limit(log(1 + exp(x))/x, x, -oo) == 0 # 267a
assert limit(log(1 + exp(x))/x, x, oo) == 1 # 267b
def test_bounded():
assert limit(sin(x)/x, x, oo) == 0 # 216b
assert limit(x*sin(1/x), x, 0) == 0 # 227a
def test_f1a():
h = Symbol("h")
#issue 3508:
assert limit((sin(2*x)/x)**(1 + x), x, 0) == 2 # Primer 7
def test_f1a2():
#issue 3509:
assert limit(((x - 1)/(x + 1))**x, x, oo) == exp(-2) # Primer 9
def test_f1b():
m = Symbol("m")
n = Symbol("n")
h = Symbol("h")
a = Symbol("a")
assert limit(sin(x)/x, x, 2) == sin(2)/2 # 216a
assert limit(sin(3*x)/x, x, 0) == 3 # 217
assert limit(sin(5*x)/sin(2*x), x, 0) == Rational(5, 2) # 218
assert limit(sin(pi*x)/sin(3*pi*x), x, 0) == Rational(1, 3) # 219
assert limit(x*sin(pi/x), x, oo) == pi # 220
assert limit((1 - cos(x))/x**2, x, 0) == S.Half # 221
assert limit(x*sin(1/x), x, oo) == 1 # 227b
assert limit((cos(m*x) - cos(n*x))/x**2, x, 0) == ((n**2 - m**2)/2) # 232
assert limit((tan(x) - sin(x))/x**3, x, 0) == S.Half # 233
assert limit((x - sin(2*x))/(x + sin(3*x)), x, 0) == -Rational(1, 4) # 237
assert limit((1 - sqrt(cos(x)))/x**2, x, 0) == Rational(1, 4) # 239
assert limit((sqrt(1 + sin(x)) - sqrt(1 - sin(x)))/x, x, 0) == 1 # 240
assert limit((1 + h/x)**x, x, oo) == exp(h) # Primer 9
assert limit((sin(x) - sin(a))/(x - a), x, a) == cos(a) # 222, *176
assert limit((cos(x) - cos(a))/(x - a), x, a) == -sin(a) # 223
assert limit((sin(x + h) - sin(x))/h, h, 0) == cos(x) # 225
def test_f2a():
assert limit(((x + 1)/(2*x + 1))**(x**2), x, oo) == 0 # Primer 8
def test_f2():
assert limit((sqrt(
cos(x)) - root3(cos(x)))/(sin(x)**2), x, 0) == -Rational(1, 12) # *184
def test_f3():
a = Symbol('a')
#issue 3504
assert limit(asin(a*x)/x, x, 0) == a
You can’t perform that action at this time.