;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!