Problem

(a) Show that $ e^x \geqslant 1 + x $ for $ x \ge…

06:57

Problem 83 Medium Difficulty

Show that $ \tan x > x $ for $ 0 < x < \pi /2 $. [Hint: Show that $ f(x) = \tan x - x $ is increasing on $ (0, \pi /2) $.]

Name: show that tan x x for 0 x pi 2 hint show that fx tan x x is increasing on 0 pi 2
Uploaded: 2020-01-15
Duration: 1 min 25 s
Channel: Numerade
Description: Show that $ \tan x > x $ for $ 0 < x < \pi /2 $. [Hint: Show that $ f(x) = \tan x - x $ is increasing on $ (0, \pi /2) $.]

Answer

$\Rightarrow \tan x>x$ for $x \in\left(0, \frac{\pi}{2}\right)$

Topics

Derivatives

Differentiation

Volume

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 3

How Derivatives Affect the Shape of a Graph

Discussion

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Catthie M.

June 18, 2021

Show that: tan(x-pi)= tan x

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Video Transcript

he has clears the wing. You married here. So we're showing that fffx, which is equal to 10 of X minus X, is increasing on zero comma pi over too. So we have the first derivative which is equal to sequence square minus one. We see that sequence square minus one is bigger than zero for all of access between zero comma pie house. So f of X is increasing for these values. So just makes off of acts to be bigger than f of zero. So tangent minus X is bigger than zero, which makes 10 gent of acts bigger than X when x from zero. Come on, pi house.

Clarissa N.

Topics

Derivatives

Differentiation

Volume

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 3

How Derivatives Affect the Shape of a Graph

Problem

(a) Show that $ e^x \geqslant 1 + x $ for $ x \ge…

Problem 83 Medium Difficulty

Show that $ \tan x > x $ for $ 0 < x < \pi /2 $. [Hint: Show that $ f(x) = \tan x - x $ is increasing on $ (0, \pi /2) $.]

Answer

$\Rightarrow \tan x>x$ for $x \in\left(0, \frac{\pi}{2}\right)$

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Heather Z.

Kayleah T.

Caleb E.

Michael J.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 4

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 2 / BC Educators

Heather Z.

Kayleah T.

Caleb E.

Michael J.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

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