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Problem

Suppose $ f $ is an odd function and is different…

03:55

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Problem 29 Easy Difficulty

Show that $ \sin x < x $ if $ 0 < x < 2\pi $.


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Leon Druch
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Fahad Paryani

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 2

The Mean Value Theorem

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Differentiation

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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.

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Problem 16
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Problem 38

Video Transcript

in this problem, we want to show that sine of X is less than X on the interval. Uh Where zero is less than X, which in turn is less than two pi. So X is in this interval from zero, not including zero up to two pi, not including two pi. So on this interval where X is between zero and two pi, we want to show that sine of X is less than X. If sine of X is less than X, that means X is greater than sign of X. And if X is greater than sign of X then x minus sine of X would have to be greater than zero. So we can show that X is greater than sign of X on this interval. Uh huh. We can show that X is greater than sign of X on this interval between zero and two pi. Uh If we can show that X minus sine of X is positive on this interval between zero and two pi remember we're not including zero because at the point X equals zero X and sine of X um are equal to each other. Uh But for X values greater than zero and less than two pi, you can see graphically uh that the function x minus sine of X is a positive function because it's graph stays above the X axis. So X minus sine of X is positive, which means X must be larger or greater than sign effects

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Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

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Lectures

Video Thumbnail

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.

Video Thumbnail

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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