Texas Instruments MathPrint TI-30X Pro

28 Math Functions
with
optional
tolerance
Classic Mode or Entry
In Classic mode or in classic edit lines, the nDeriv( command will paste from the
keypad or MATH menu.
Syntax: nDeriv(expression,variable,point[,tolerance]) where tolerance is optional and
the default H is 1EM5.
Example
% A
or
d
MATH
7:nDeriv(
% A
z F T 5 z
% ` z
% ` M 1 )
<
About the Numerical Derivative at a Point
The numerical derivative at a point command, nDeriv( or d/dx, uses the symmetric
difference quotient method. This method approximates the numerical derivative at a
given point as the slope of the secant line about the point.
( )
f x′ =
f x ε f x ε
ε
(
+
)
−
(
−
)
2
As H becomes smaller, the approximation usually becomes more accurate to
approximate the slope of the tangent line at the given point x.
• Because of the method used to calculate the numerical derivative at a point, the
calculator can return a false derivative value at a non-differentiable point.
• Always have some knowledge of the function behaviour near the point by using a
table of values near the point (or a graph of the function).
³ Problem
Find the slope of the tangent line to the function f(x) = x
2
- 4x at x = 2. What do you
notice?
% A
z F U 4 z " "
2 <
Numerical Integral
The TI-30X Pro MathPrint™ calculates the (approximate) numerical integral of an
expression with respect to a variable x, given a lower limit, an upper limit and a
tolerance for the numerical method.