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The figure shows a line $ L_1 $ in space and a se…

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Problem 42 Easy Difficulty

The solid upper hemisphere of the sphere of radius 2 centered at the origin


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Related Courses

Calculus 3

Calculus: Early Transcendentals

Chapter 12

Vectors and the Geometry of Space

Section 1

Three-Dimensional Coordinate Systems

Related Topics

Vectors

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Lectures

Video Thumbnail

02:56

Vectors Intro

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

Video Thumbnail

11:08

Vector Basics Overview

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

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Problem 13
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Problem 15
Problem 16
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Problem 24
Problem 25
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Problem 31
Problem 32
Problem 33
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Problem 36
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Problem 38
Problem 39
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Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48

Video Transcript

Yeah, let's write mathematical statements that define the region of the upper hemisphere of the solid sphere centered at the origin with radius too. So the silence here, Senator, the origin with radius too. It's gonna be a sphere right here. The boundary of that sphere. It's gonna have the equation X square plus why square plus the square equals two square. But we don't just want the edge of this year. We want this solid sphere. Yes, we want that and all the points on the inside X Where? Let's slice where, plus the square, less than or equal 24 But we only want the upper half. So you want to cut it off right here along this circle and not include the bottom half? Well, that's an extra restriction just on Z. We're forcing Z to be non negative and so we still want all the points inside the sphere with the added a requirement that Z can't be negatives and that will give us region that we want

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Top Calculus 3 Educators
Catherine Ross

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Lectures

Video Thumbnail

02:56

Vectors Intro

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

Video Thumbnail

11:08

Vector Basics Overview

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

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