
Concept explainers
Problems 87-94 require the following discussion of a secant line. The slope of the secant line containing the two points and on the graph of a function may be given as
(a) Express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer.
(b) Find msec for , 0.1, and 0.01 at . What value does msec approach as h approaches 0?
(c) Find an equation for the secant line at with .
(d) Use a graphing utility to graph f and the secant line found in part (c) in the same viewing window.
88.

To find: The following values using the given function .
a. Express and simplify the slope of the secant line of function in terms of and .
Answer to Problem 82AYU
a. is the slope of the secant line of function .
Explanation of Solution
Given:
The function is given as .
Calculation:
It requires the discussion of a secant line.
The slope of the secant line containing the two points and on the graph of a function may be given as,
a. Slope of the secant line of function ,

To find: The following values using the given function .
b. for , and at .
Answer to Problem 82AYU
b. for , and at approaches 0 are .
Explanation of Solution
Given:
The function is given as .
Calculation:
It requires the discussion of a secant line.
The slope of the secant line containing the two points and on the graph of a function may be given as,
b. for and .
for and .
for and .
As approaches 0, .

To find: The following values using the given function .
c. An equation for the secant line with .
Answer to Problem 82AYU
c. is the equation for the secant line at with .
Explanation of Solution
Given:
The function is given as .
Calculation:
It requires the discussion of a secant line.
The slope of the secant line containing the two points and on the graph of a function may be given as,
c. An equation for the secant line at with .
The points are and and .
Equation of a straight line with two points .

To find: The following values using the given function .
d. Graph the function and the secant line found in part .
Answer to Problem 82AYU
d.
Explanation of Solution
Given:
The function is given as .
Calculation:
It requires the discussion of a secant line.
The slope of the secant line containing the two points and on the graph of a function may be given as,
d.
Chapter 2 Solutions
Precalculus
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