Chapter 6: Q. 41 (page 419)

find the average rate of change of f from $0$ to $\frac{π}{6}$
role="math" localid="1646337271984" $f (x) = \tan x$
.

Short Answer

Expert verified

the average rate of change of $f (x) = \tan x$ from $0$ torole="math" localid="1646337601973" $\frac{π}{6}$ is $\frac{2 \sqrt{3}}{π}$

Step by step solution

Step 1. Given data

The given function is

$f (x) = \tan x$

The given range isrole="math" localid="1646337698106" $[a, b] = [0, \frac{π}{6}]$

Step 2. average rate of change

the average rate of change f

$\frac{f (b) - f (a)}{b - a} = \frac{\tan (b) - \tan (a)}{b - a} = \frac{\tan (\frac{π}{6}) - \tan (0)}{\frac{π}{6} - 0} = \frac{\frac{1}{\sqrt{3}} - 0}{\frac{π}{6}} = \frac{2 \sqrt{3}}{π}$

So average rate of change is $\frac{2 \sqrt{3}}{π}$

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find the average rate of change of f from $0$ to $\frac{π}{6}$
role="math" localid="1646337271984" $f (x) = \tan x$
.

Short Answer

Step by step solution

Step 1. Given data

Step 2. average rate of change

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find the average rate of change of f from 0toπ6role="math" localid="1646337271984" f(x)=tanx.

Short Answer

Step by step solution

Step 1. Given data

Step 2. average rate of change

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

Statistics

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

find the average rate of change of f from $0$ to $\frac{π}{6}$
role="math" localid="1646337271984" $f (x) = \tan x$
.