# Limits of a first-year calculus course: "f; x0[; dir]" (dir: plus/minus).
# make_limits.py runs Maxima (what Sage's limit calls) on each.
sin(x)/x; 0
(1 - cos(x))/x^2; 0
(exp(x) - 1)/x; 0
log(1 + x)/x; 0
tan(x)/x; 0
(x^2 - 1)/(x - 1); 1
(x^3 - 8)/(x - 2); 2
(sqrt(x + 4) - 2)/x; 0
(sqrt(1 + x) - 1)/x; 0
x*sin(1/x); 0
x^2*sin(1/x); 0
x*log(x); 0; plus
x^x; 0; plus
(1 + x)^(1/x); 0
(1 + 1/x)^x; oo
(1 + 2/x)^x; oo
(1 - 1/x)^x; oo
x/exp(x); oo
x^10/exp(x); oo
exp(x)/x^5; oo
log(x)/x; oo
log(x)/sqrt(x); oo
x*exp(-x); oo
(3*x^2 + 2)/(5*x^2 - x); oo
(2*x^3 + x)/(x^2 + 1); oo
(x + 1)/(x^2 + 1); oo
sqrt(x^2 + x) - x; oo
sqrt(x^2 + 1) - sqrt(x^2 - 1); oo
x - sqrt(x^2 - 3*x); oo
x*sin(1/x); oo
x*(exp(1/x) - 1); oo
arctan(x); oo
arctan(x); -oo
exp(-x)*sin(x); oo
1/x; 0; plus
1/x; 0; minus
1/x^2; 0
exp(1/x); 0; minus
exp(1/x); 0; plus
abs(x)/x; 0; plus
abs(x)/x; 0; minus
(sin(x) - x)/x^3; 0
(tan(x) - x)/x^3; 0
(exp(x) - 1 - x)/x^2; 0
(cos(x) - 1 + x^2/2)/x^4; 0
(1/x - 1/sin(x)); 0
1/x - 1/(exp(x) - 1); 0
(2^x - 1)/x; 0
sin(3*x)/sin(5*x); 0
(x - sin(x))/(x - tan(x)); 0
log(x)^2/x; oo
x^(1/x); oo
(x^2 + 1)^(1/log(x)); oo
sin(x)/x; oo
cos(x)^(1/x^2); 0
(1 + sin(x))^(1/x); 0
x^(1/(1 - x)); 1
(exp(x) + x)^(1/x); oo
exp(x)*(exp(1/x - exp(-x)) - exp(1/x)); oo
log(log(x))/log(x); oo
x^2*exp(-x^2); oo
(x^3 - 2*x)/(x + 1)^3; -oo
