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Problem

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

06:57

Question

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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) $.]

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Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 3

How Derivatives Affect the Shape of a Graph

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Catthie M.

June 18, 2021

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

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Lectures

04:35

Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

06:14

Review

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

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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.

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