; Computing the slope of x^3 via a limit from above
LIM (((x + h)^3 - x^3) / h, h, 0)
; A famous limit of an indeterminate form 0/0
LIM (SIN x / x, x, 0)
; A limit as x approaches infinity
LIM (x^(1/x), x, inf)
; A limit involving extra variables
LIM ((a^x - b^x) / x, x, 0)
; The limit of 1/x as x approaches 0 from below
LIM (1/x, x, 0, T)
; 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)

; The formula for the slope of x^3
DIF (x^3, x)
; An illustration of the chain rule
DIF (sin (x^3), x)
; A partial derivative
DIF (x^2 y^3, y)

; A 5th-order Taylor polynomial expanded about x=0
TAYLOR (#e^x, x, 0, 5)
; A 7th-order Taylor polynomial
TAYLOR (LN COS (a x), x, 0, 7)

; An antiderivative of x^2 with respect to x
INT (x^2, x)
; An antiderivative of cosine(x) with respect to x
INT (COS x, x)
; An antiderivative by substituting a x^3 + b --> u
INT (x^2 COS (a x^3 + b), x)
; A definite integral for x going from a to b
INT (x^2, x, a, b)
; An integral having an infinite integration limit
INT (1/x^2, x, a, inf)
; An integral having an endpoint singularity
INT (1/SQRT x, x, 0, b)
; A 2-dimensional integral over a quarter disk
INT (INT (x y, y, 0, SQRT (r^2 - x^2)), x, 0, r)

; The formula for the sum of an arithmetic series
SUM (k, k, 0, n)
; The formula for the sum of successive cubes
SUM (k^3, k, 0, n)
; The formula for the sum of a geometric series
SUM (a^k, k, 0, n)
; The sum of an infinite series
SUM (2^-k, k, 0, inf)
; A sum for which iteration would be slow
SUM (k/370370367, k, -123456788, 123456789)

; The product of successive even integers
PRODUCT (2 k, k, 1, n)
