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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 6: Q. 43 (page 419)

find the average rate of change of f from $0$ to $\frac{蟺}{6}$
role="math" localid="1646338076356" $f (x) = \tan (2 x)$
.

Short Answer

Expert verified

the average rate of change of f $f (x) = \tan (2 x)$ from $0$ to $\frac{蟺}{6}$ is $\frac{6 \sqrt{3}}{蟺}$

Step by step solution

01

Step 1. Given data

The given function is

$f (x) = \tan (2 x)$

The given range is $[a, b] = [0, \frac{蟺}{6}]$

02

Step 2. average rate of change

The average rate of change f

$\frac{f (b) - f (a)}{b - a} = \frac{\tan (2 b) - \tan (2 a)}{b - a} = \frac{\tan (2 脳 \frac{蟺}{6}) - \tan (2 脳 0)}{\frac{蟺}{6} - 0} = \frac{\tan \frac{蟺}{3} - \tan 0}{\frac{蟺}{6}} = \frac{\sqrt{3} - 0}{\frac{蟺}{6}} = \frac{6 \sqrt{3}}{蟺}$

So average rate of change is $\frac{6 \sqrt{3}}{蟺}$

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Most popular questions from this chapter

A __________ __________ is a positive angle whose vertex is at the center of a circle.

Covert each angle in degrees to radians. Express your answer as a multiple of $蟺$ .

What is the formula for the circumference $C$ of a circle of radius $r$ ? What is the formula for the area $A$ of a circle of radius $r$ ?

For a circle of radius r, a central angle of u degrees subtends an arc whose length s is $s = \frac{蟺}{180} r 胃$ . Discuss whether this is a true or false statement. Give reasons to defend your position.

graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y = 2 c s c (\frac{1}{3} x) - 1$

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