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Sketch the curve with the given vector equation. Indicate with an arrow the direction in which $ t $ increases.

$ r(t) = \cos t i - \cos t j + \sin t k $

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Calculus 3

Chapter 13

Vector Functions

Section 1

Vector Functions and Space Curves

Missouri State University

Harvey Mudd College

Idaho State University

Boston College

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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Sketch the curve with the …

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the problem is sketch of the curve with given back to the equation indicated with pero the direction engaged increases. You're Artie. If people to assign teatime sine minus cosigned, have still assigned, you have Okay, so we have access to assign you. Why is this call to negative signs saying Yes. He called you fine. So we have axe you, couldn't you? Negative. Why? And x squared plus c squared. It's equal to what now? First we can gather playing X. It was connected. Why? Then we can drive there. Circle X squared plus two squared equals one answer plane acts before to next. Why now? Let's catch the curve. It's a plane axe. You could have connected. Why is this plane now? Let's draw a circle. I screamed like this. Why you would want this Now let's see what he is. They go to zero. We have Max. Why? Why could nick one and say to you zero So this point and what he go to Hyo went to have actually but wife with zero and saying too wants this point. So the direction in which tea increases is this direction

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