uΠ [Action][Calculation][Π]

Function: Evaluates an expression at discrete variable values within a range, and then calculates a product.

Syntax: Π(Exp/List, variable, lower value, upper value [ ) ]

Example: To calculate the product of x2 as the value of x changes from x = 1 through x = 5

urangeAppoint [Action][Calculation][rangeAppoint]

Function: Finds an expression or value that satisfies a condition in a specified range.

Syntax: rangeAppoint (Exp/Eq/List, start value, end value [ ) ]

•When using an equation (Eq) for the first argument, input the equation using the syntax Var = Exp. Evaluation will not be possible if any other syntax is used.

Example: To find the expression(s) in the list {x = π, x = 2π,

x = 3π} that belong(s) to the closed range 0 s x s 5

umod [Action][Calculation][mod]

Function: Returns the remainder when one expression is divided by another expression.

Syntax: mod ({Exp/List} -1, {Exp/List} -2 [ ) ]

Example: To determine the remainder when 26 is divided by 3 (26mod3)

utanLine [Action][Calculation][line][tanLine]

Function: Returns the right side of the equation for the tangent line (y = ‘expression’) to the curve at the specified point.

Syntax: tanLine (Exp/List, variable, variable value at point of tangency [ ) ]

Example: To determine the function of the line tangent to y = x3 at x = 2

unormal [Action][Calculation][line][normal]

Function: Returns the right side of the equation for the line normal (y = ‘expression’) to the curve at the specified point.

Syntax: normal (Exp/List, variable, variable value at point of normal [ ) ]

Example: To determine the function of the line normal to y = x3 at x = 2

uarcLen [Action][Calculation][line][arcLen]

Function: Returns the arc length of an expression from a start value to an end value with respect to a specified variable.

Syntax: arcLen (Exp/List, variable, start value, end value [ ) ]

3

Example: To determine the arc length for y = x 2 from x = 0 to x = 4

ufMin [Action][Calculation][fMin/fMax][fMin], fMax [Action][Calculation][fMin/fMax][fMax]

Function: Returns the minimum (fMin) / the maximum (fMax) point in a specific range of a function.

Syntax: fMin(Exp[,variable] [ ) ]

fMin(Exp, variable, start value, end value[,n] [ ) ] fMax(Exp[,variable] [ ) ]

fMax(Exp, variable, start value, end value[,n] [ ) ]

•“x” is the default when you omit “[,variable]”.

•Negative infinity and positive infinity are the default when the syntax fMin(Exp[,variable] [ ) ] or fMax(Exp[,variable] [ ) ] is used.

Chapter 2: Main Application

66