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