┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 8.6, Release Date: 2019-01-15 │
│ Using Python 2.7.15. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
sage: f=exp(-2*x^2)-cos(2*x);f
-cos(2*x) + e^(-2*x^2)
sage: g=x*(sin(x))^3;g
x*sin(x)^3
sage: lim(f/g,x=0) # this is wrong
und
sage: lim(f/g,x=0,dir='-'),lim(f/g,x=0,dir='+') # the second result is wrong
(4/3, +Infinity)
sage: taylor(f/g,x,0,3) # this is right
-26/45*x^2 + 4/3
sage: lim(f/x^4,x=0) # this is right too
4/3
sage: