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

$ r(t) = t^2 i + t^4 j + t^6 k $

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Calculus 3

Chapter 13

Vector Functions

Section 1

Vector Functions and Space Curves

Campbell 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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the problem. These sketches a curve with give a lecture equation indicated with heralds the direction in which to increases your heart. He is a twenty square pasa homes I plus city for a steel and plastic to six. Okay, Behalf acts is a country squire. Why is he going to do teach force and cnc country? It is the power of six Now we have Why is he going to export now Let's catch the curve. Says why is he goto x square? So we know the projection of the curve on the X Y plane is why go to explain? So can job. Why, his secret was I could square It's like this and then that won t is equal to zero We have two point zero zero zero tz four to one. So we have this point. She could too half this point this former team three transit point. Now we can just a graph this like this on offense Axe is hard to describe. Why single pretty to force the direction in which team increases is this direction

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