;Computing the slope of x^3 via a limit
LIM(((x+h)^3-x^3)/h,h,0)
3*x^2
;A famous limit of an indeterminate form 0/0
LIM(SIN(x)/x,x,0)
1
;A limit as x approaches infinity
LIM(x^(1/x),x,inf)
1
;A limit involving extra variables
LIM((a^x-b^x)/x,x,0)
LN(a)-LN(b)
;The limit of 1/x as x approaches 0 from the left
LIM(1/x,x,0,-1)
-inf
;A limit for which L'Hopital's rule would be slow
LIM(SIN(x)^249*LN(1-x)^251/(x^100*ATAN(x)^400),x,0)
-1
;The formula for the slope of x^3
DIF(x^3,x)
3*x^2
;An illustration of the chain rule
DIF(SIN(x^3),x)
3*x^2*COS(x^3)
;A partial derivative
DIF(x^2*y^3,y)
3*x^2*y^2
;A 5th-order Taylor polynomial expanded about x=0
TAYLOR(#e^x,x,0,5)
0.00833333*x^5+0.0416666*x^4+0.166666*x^3+0.5*x^2+x+1
;A 7th-order Taylor polynomial
TAYLOR(LN(COS(a*x)),x,0,7)
-0.0222222*a^6*x^6-0.0833333*a^4*x^4-0.5*a^2*x^2
;An antiderivative of x^2 with respect to x
INT(x^2,x)
0.333333*x^3
;An antiderivative of cosine(x) with respect to x
INT(COS(x),x)
SIN(x)
;An antiderivative obtained by substitution
INT(x^2*COS(a*x^3+b),x)
0.333333*SIN(b)*COS(a*x^3)/a+0.333333*COS(b)*SIN(a*x^3)/a
;A definite integral for x going from a to b
INT(x^2,x,a,b)
0.333333*b^3-0.333333*a^3
;An integral having an infinite integration limit
INT(1/x^2,x,a^2,inf)
1/a^2
;An integral having an endpoint singularity
INT(1/SQRT(x),x,0,b^2)
2*ABS(b)
;A 2-dimensional integral over a quarter disk
INT(INT(x*y,y,0,SQRT(r^2-x^2)),x,0,r)
0.125*r^4
;The formula for the sum of an arithmetic series
SUM(k,k,0,n)
0.5*n*(n+1)
;The formula for the sum of successive cubes
SUM(k^3,k,0,n)
0.25*n^2*(n+1)^2
;The formula for the sum of a geometric series
SUM(a^k,k,0,n)
a^(n+1)/(a-1)-1/(a-1)
;The sum of an infinite series
SUM(2^(-k),k,0,inf)
2
;A sum for which iteration would be slow
SUM(k/370370367,k,-123456788,123456789)
0.333333
;The product of successive even integers
PRODUCT(2*k,k,1,n)
2^n*n!