Tables of Values and Plots
The following limit is of special interest. We examine the behavior of this
function near 0.
Evaluate

= 1
You can generate a table of values by applying a function to a vector of
domain values and then concatenating matrices, or you can do it in one step
by defining appropriate auxiliary functions. Following are examples of each.
To create a table of values for the function y = f (x)
by defining auxiliary functions
- Define the function f (x)
- Define a function g(n) that will provide a sample of values of the
independent variable.
- Define the function
h(i, j) = (2 - j)g(i) + (j - 1)f (g(i))
- From the Matrices submenu, choose Fill Matrix.dtbpF3.5051in2.06in0ptfillmat2.wmf
- Set Columns to 2, and and set Rows to match the
size of your sample.
- Under Fill With, choose Defined By Function.
- In the input box for function name, enter h.
- Choose OK.
To create a table of values for the function y = sin x
- With the insertion point in the equation
f (x) = sin x, choose
Define + New Definition.
- With the insertion point in the equation
g
i
= i * 10-2, choose Define + New Definition.
- With the insertion point in the equation
h(i, j) = (2 - j)g(i) + (j - 1)f (g(i)), choose Define + New Definition.
- Choose expanding brackets and leave the insertion point in the input
box.
- From the Matrices submenu, choose Fill Matrix.
- Set Columns to 2, and and set Rows to 10.
- Under Fill With, choose Defined By Function.
- In the input box for function name, enter h.
- Choose OK.
The result is the matrix below on the left. To get the matrix on the right,
choose Evaluate Numerically.
To generate a table of values by
concatenating matrices
- 1.
- Click itbpF0.3009in0.3009in0.0701inmatrix.wmf (or
choose Insert + Matrix)
- 2.
- Choose one column and any number of rows.
- 3.
- Fill in domain values in the rows.
- 4.
- Put parentheses around the matrix.
- 5.
- Evaluate f (your matrix).
It is also useful to examine the graph of
y =
on an
interval containing 0. The graph gives additional strong evidence that

= 1.
Plot 2D + Rectangular
dtbpFU3in2.0003in0pt
y =