26.7: A.7- Special functions (absolute value, n-th root, etc.)
- Page ID
- 54494
We now point out some important functions in the MATH menu (\(\boxed{\text{math}}\)) and the LIST menu (\(\boxed{\text{2nd}}\)\(\boxed{\text{stat}}\)), that are used in this course.
Fractions
Suppose in the main screen you evaluate \(4/6\). Your calculator will display \(.66666666667\). If you wanted to see this as a fraction you would type \(\boxed{\text{math}}\)\(\boxed{\text{enter}}\)\(\boxed{\text{enter}}\). You will now see \(2/3\) displayed.
Absolute value
To evaluate \(|-4|\) you would type in the main screen \(\boxed{\text{math}}\)\(\boxed{\triangleright}\)\(\boxed{\text{enter}}\)\(\boxed{\text{(-)}}\)\(\boxed{\text{4}}\)\(\boxed{\text{enter}}\). The answer \(4\) should be displayed. To graph \(|x-2|\), go to the Y= screen (\(\boxed{y=}\)) and enter in the Y1 (for example) space \(\boxed{\text{math}}\)\(\boxed{\triangleright}\)\(\boxed{\text{enter}}\)\(\boxed{\text{X,T,}\theta,n}\)\(\boxed{\text{-}}\)\(\boxed{\text{2}}\)\(\boxed{\triangleright}\)\(\boxed{\text{enter}}\).
Now you can go to the graphing screen to see the graph.
\(n\)-th root
To calculate the cube root of \(8\). Press on the main screen \(\boxed{\text{3}}\)\(\boxed{\text{math}}\)\(\boxed{\text{5}}\) (or select the x-root) \(\boxed{\text{8}}\)\(\boxed{\text{enter}}\).
You can compute any root this way (e.g. the \(5\)th root of \(7\)). For the cube root you can also use \(\boxed{\text{math}}\)\(\boxed{\text{4}}\) instead. Recall also the algebraic definition of the \(n\)th root,
\[\sqrt[n]{x}=x^{\frac{1}{n}} \nonumber \]
so that the \(5\)th root of \(7\) can also be computed by pressing \(\boxed{\text{7}}\)\(\boxed{\wedge}\)\(\boxed{\text{(}}\)\(\boxed{\text{1}}\)\(\boxed{\div}\)\(\boxed{\text{5}}\)\(\boxed{\text{)}}\).
Factorials
To compute \(5!\), for example, in the main screen type \(\boxed{\text{5}}\)\(\boxed{\text{math}}\) then move the cursor to the right three times (or left once) so that the ’PRB’ menu is displayed. Option 4 is ’\(!\)’ so press \(\boxed{\text{4}}\) or move the cursor to highlight this option and press \(\boxed{\text{enter}}\). Finally press \(\boxed{\text{enter}}\) and the answer \(120\) will be displayed.
Combinations and permutations
To calculate \(_{5} C_{2}=\dbinom{5}{2}\), in the main menu type \(\boxed{\text{5}}\). Then go to the math-probability menu by pressing \(\boxed{\text{math}}\) then the right (or left) arrow until ’PRB’ is highlighted. You will see that the third option is \(_nC_r\) so press \(\boxed{\text{3}}\). This will return you to the main screen. Press \(\boxed{\text{2}}\)\(\boxed{\text{enter}}\). The answer \(10\) will be displayed.
Permutations \(_nP_r\) are handled the same way except it is the second option under the math-probability menu instead of the third.
Sequences and series
A sequence \(a_1,a_2,a_3,\dots\) that is given by a formula can be added via the ‘LIST’ menu (press \(\boxed{\text{2nd}}\)\(\boxed{\text{stat}}\)). For example, to enter the first \(10\) terms \(a_1,a_2,\dots, a_{10}\) of the sequence \(a_n=n^2+1\), we have to write \(seq(x^2+1,x,1,10)\). Here, the ‘sequence’ command takes four inputs, first the assignment \(x^2+1\), second the independent variable \(x\), third the starting index \(1\), and fourth the final index \(10\). This expression is entered to the calculator by pressing \(\boxed{\text{2nd}}\)\(\boxed{\text{stat}}\)\(\boxed{\triangleright}\)\(\boxed{\text{5}}\)\(\boxed{\text{X,T,}\theta,n}\)\(\boxed{x^2}\)\(\boxed{\text{+}}\)\(\boxed{\text{1}}\)\(\boxed{\text{,}}\)\(\boxed{\text{X,T,}\theta,n}\)\(\boxed{\text{,}}\)\(\boxed{\text{1}}\)\(\boxed{\text{,}}\)\(\boxed{\text{1}}\)\(\boxed{\text{0}}\)\(\boxed{\text{)}}\) and then confirmed by pressing \(\boxed{\text{enter}}\). We obtain:
To add the ten numbers \(a_1+\dots +a_{10}\) of the sequence, we use the ‘sum’ command in the LIST-MATH menu. Press \(\boxed{\text{2nd}}\)\(\boxed{\text{stat}}\)\(\boxed{\triangleleft}\)\(\boxed{\text{5}}\) to enter the ‘\(sum(\)’ expression. Then using the previously entered answer by pressing \(\boxed{\text{2nd}}\)\(\boxed{\text{(-)}}\), and finishing with \(\boxed{\text{)}}\)\(\boxed{\text{enter}}\), we now calculate the wanted sum.