Education Technology

# Knowledge Base

## Solution 35914: Calculating the Central Difference Quotient of an Expression on the TI-Nspire™ CAS Family.

### How do I calculate the Central Difference quotient of an expression on the TI-Nspire CAS family?

Use the centralDiff() formula to calculate expression, list, and matrix. This function is found under [catalog]. The syntax is as follows:

centralDiff(Exp, Var[=Value][,Step])

These examples are done in Radian mode of a calculator App, to change the settings to Radian please do the following:

1) Press [home] and choose to add a Calculator.
2) Press [doc] [7] [2].
3) Press [▼] [►] select Radian and press [enter] [enter].

When using the central difference quotient formula it returns the numerical derivative.

1) Press [catalog] [C] and scroll down to centralDiff( and press [enter].

2) Press [trig] [►] [enter].
3) Press [X] [►].
4) Press [,] [X] [,] [H] [enter].
5) Press [catalog] [L] and scroll down to lim( and press [enter].
6) Press [catalog] [C] and scroll down to centralDiff( and press [enter].
7) Press [trig] [►] [enter].
8) Press [X] [►].
9) Press [,] [X] [,] [H].
10) Press [►] [,] [H] [,] [0] [enter].

When value is specified, it overrides any prior variable assignment or any current “I” substitution for the variable. Step is the step value. If step is omitted, it defaults to 0.001.

1) Press [catalog] [C] and go down to centralDiff( and press [enter].
2) Press [X] [^] [3] [►].
3) Press [,] [X] [,] [0] [.] [0] [1] [enter].
4) Press [catalog] [C] and down to centralDiff( and press [enter].
5) Press [trig] [►] [enter].
6) Press [X] [►] [,] [X] [►].
7) Press [ctrl] [|] [►] [►] [▼] [enter].
8) Press [X] [=] [Pi] [enter] [/] [2] [enter].

When using List1 or Matrix1, the operation gets mapped across the values in the list or across the matrix elements.

1) Press [catalog] [C], scroll to centralDiff(, and press [enter].
2) Press [X] [x2] [,] [X] [,].
3) Press [ctrl] [{].
4) Press [0] [.] [0] [1] [,] [0] [.] [1] [enter].