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Problem

Find three different surfaces that contain the cu…

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Problem 28 Hard Difficulty

Show that the curve with parametric equations $ x = \sin t $, $ y = \cos t $, $ z = \sin^2 t $ is the curve of intersection of the surfaces $ z = x^2 $ and $ x^2 + y^2 = 1 $. Use this fact to help sketch the curve.

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Calculus 3

Calculus: Early Transcendentals

Chapter 13

Vector Functions

Section 1

Vector Functions and Space Curves

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Vector Valued Functions - Intro

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x. The input of a function is called the argument and the output is called the value. The set of all permitted inputs is called the domain of the function. Similarly, the set of all permissible outputs is called the codomain. The most common symbols used to represent functions in mathematics are f and g. The set of all possible values of a function is called the image of the function, while the set of all functions from a set "A" to a set "B" is called the set of "B"-valued functions or the function space "B"["A"].

08:32

Vector Valued Functions and Curves - Overview

In mathematics, vector calculus is an important part of differential geometry, together with differential topology and differential geometry. It is also a tool used in many parts of physics. It is a collection of techniques to describe and study the properties of vector fields. It is a broad and deep subject that involves many different mathematical techniques.

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Video Transcript

The problem is show that is a curve for its parametric equations x. Equal to sine t y is equal to sine t. 3 is equal to sine t square is a curve of intersection of the surfaces 3 equal to x, squared and x, squared plus y squared is equal to 1. I use this fact to help sketch the curve. So first the relation between x and wat and z have x is sin is equal to sine square, so we have is equal to x, coined and x. Squared plus y squared is equal to sine t square plus sine t square, so this is equal to 1. So behalf, the curve is a curve of intersection of the surfaces equal to x, squared and x, squared plus y squared equals to 1 point now. Let'S sketch the curve, the first we draw the sin or x, squared plus y squared is equal to 1, and then we choose some points on the curve, so 0100 negative, 10 and 101 negative 101 at the point of 101. Is this point and 0 negative 10? This point and 101 is this point and 1 negative 10 poison. The graph is like this is a graph of the.

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