### Expressions in Mathlets

The expressions entered into the text fields may include any combination of the following:
• x + y: addition
• x - y: subtraction
• x * y: multiplication
• In many situations, the asterisk "*" is not necessary in multiplication expressions -- for example, the expression "2pi" is correct. For this sort of expression, the first factor in the product must be a number; the second factor must be a variable (as in "2x"), a constant ("2pi"), a function ("2sin(x)"), or an expression enclosed in parentheses ("2(x+y)"). Note in particular that expressions such as "xy" or "xsin(x)" are not correct.
• x / y: division
• x ^ y: exponentiation (xy)
• ( ... ): grouping
• decimal numbers, e.g. 5.317
• pi: constant (3.1416...)
• e: constant (2.7183...)
• infty: constant (infinity -- used with conditional expression to delete part of a graph)
• x, y, z, r, s, t, u, v, n, c: free variables (availability depends on applet)
• sin(x): sine function
• cos(x): cosine function
• tan(x): tangent function
• sec(x): secant function
• csc(x): cosecant function
• cot(x): cotangent function
• arcsin(x): arcsine function
• arccos(x): arccosine function
• arctan(x): arctangent function
• arcsec(x): arcsecant function
• aliases: asin for arcsin,
acos for arccos,
atan for arctan,
asec for arcsec
• exp(x): natural exponential function (ex)
• ln(x): natural logarithm function
• log(x): logarithm base 10
• abs(x): absolute value function
• sqrt(x): square root function
• nrt(n,x): nth root function
• int(x): greatest integer function (returns greatest integer less than or equal to x)
• alt(x): sign alternation function (returns 1 if int(x) is even, -1 if int(x) is odd) -- can be used to establish alternation of terms in series without using computationally expensive "(-1)^n" expression
• max(x, y): maximum of x and y
• min(x, y): minimum of x and y
• n !: factorial of n
• x ? y : z: conditional expression, returns value y if x>0, z otherwise
• x < y: boolean relation, returns value 1.0 if x<y, 0.0 otherwise
• x > y: boolean relation, returns value 1.0 if x>y, 0.0 otherwise
• x = y: boolean relation, returns value 1.0 if x=y,0.0 otherwise
• x & y: logical AND connective, returns value 1.0 if x>0 and y>0, 0.0 otherwise
• x | y: logical OR connective (inclusive), returns value 1.0 if x>0 or y>0 (or both), 0.0 otherwise
• ~ x: logical NOT operator, returns value 1.0 if not x>0, 0.0 otherwise