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- ;Computing the slope of x^3 via a limit
- 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 the left
- LIM (1/x, x, 0, -1)
- ;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)
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- ;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)
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- ;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)
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- ;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 obtained by substitution
- 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^2, inf)
- ;An integral having an endpoint singularity
- INT (1/SQRT x, x, 0, b^2)
- ;A 2-dimensional integral over a quarter disk
- INT (INT (x y, y, 0, SQRT (r^2 - x^2)), x, 0, r)
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- ;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)
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- ;The product of successive even integers
- PRODUCT (2 k, k, 1, n)
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