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Find a vector function that represents the curve of intersection of the two surfaces.

The cylinder $ x^2 + y^2 = 4 $ and the surface $ z = xy $

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$<2 \cos (t), 2 \sin (t), 4 \sin (t) \cos (t)>$

Calculus 3

Chapter 13

Vector Functions

Section 1

Vector Functions and Space Curves

Missouri State University

Campbell University

Harvey Mudd College

Baylor University

Lectures

03:04

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

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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Find a vector function tha…

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Find it a factory function that represents the curve of intersection of the 2 surfaces. The sin in the x, squared plus y square is equal to 4 and the surface z is equal to x, mine. So from the sin jer x, squared plus y squared equal to 4, we can write x is equal to 2 cosine. T y is equal to 2 sine t, then, by the surface, z is equal to x y. So we can add, t is equal to 2 cosine t tims to cosine sine t, so this is equal to 2 times sine 2. Now the wat to function, r t is equal to 2 cosine t 2 sine t and 2 sine 2 t. This is a wictim function that represents a curve of intersection, ces.

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