# TI-83 Plus Math MATH Submenu

Press **[MENU]** to access the Math MATH submenu on the TI-83 Plus graphing calculator. This submenu contains general mathematical functions you can insert into an expression.

## How to convert between decimals and fractions

The **Frac** function always converts a finite decimal to a fraction. Sometimes this function can convert an infinite repeating decimal to a fraction. When it can’t, it lets you know by redisplaying the decimal. Be sure to enter the decimal before inserting the **Frac** function, as shown in the first two lines of the first picture.

The **Dec** function converts a fraction to a decimal. Enter the fraction before you insert the **Dec** function.

## How to take cube roots on TI-83

The cube function, ** ^{3}**, cubes the value that precedes the function. The cube-root function,

finds the cube root of a value that follows the function. This value must be enclosed in parentheses; the calculator supplies the opening parenthesis; you must supply the closing parenthesis.

## How to take the *x*th root

The *x*th root function

finds the *x*th root of the value that follows the function. To use this function, first enter the root *x*, then insert the

function, and then enter the argument. In this example the calculator is evaluating the fourth root of 16.

## How to find the location of maximum and minimum values

The **fMin** and **fMax **functions on the TI-83 Plus approximate *where* the minimum or maximum value of a function occurs in a specified interval. *They do not compute the minimum or maximum value of the function*; they just give you the *x*-coordinate of the minimum or maximum point.

The **fMin** and **fMax **functions are standalone functions in the sense that they cannot be used in an expression. To use these functions, insert the appropriate function, **fMin** or **fMax,** at the beginning of a new line on the Home screen. Then enter the definition of the function whose minimum or maximum you want to locate.

Press **[,]** and enter the variable used in the definition of the function you just entered. Press **[,]** and enter the lower limit of the specified interval. Then press **[,]**, enter the upper limit, and press **[**** ) ****]**. Finally, press **[ENTER]** to *approximate* the location of the minimum or maximum in the specified interval.

## How to do numerical differentiation and integration

The TI-83 Plus calculator cannot perform symbolic differentiation and integration. For example, it cannot tell you that the derivative of *x*^{2} is 2*x*, nor can it evaluate an indefinite integral. But the **nDeriv** function will approximate the derivative (slope) of a function at a specified value of the variable, and the **fnInt** function will approximate a definite integral.

Insert the **nDeriv** function, enter the function whose derivative you want to find, and then press **[,]**. Enter the variable used in the definition of the function you just entered and press **[,]**. Then enter the value at which the derivative is to be taken, and press **[**** ) ****]**. Finally, press **[ENTER]**** **to *approximate* the derivative.

To use the **fnInt** function, insert **fnInt**, and then enter the function you are integrating. Press **[,]** and enter the variable used in the definition of the function you just entered. Press **[,]** and enter the lower limit of the definite integral. Press **[,]**, enter the upper limit, and press **[**** ) ****]**. Finally, press **[ENTER]** to *approximate* the definite integral.

The calculator may give you an error message or a false answer if **nDeriv** is used to find the derivative at a nondifferentiable point or if **fnInt** is used to evaluate an improper integral.