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CalculusMultivariable Calculus8th Edition

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Chapter 13.1, Problem 13E
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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 49E
Problem 50E
Problem 53E
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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

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

13. r(t) = t2 i + t4 j + t6 k

To determine

To sketch: the curve of vector equation r(t)=t2i+t4j+t6k and indicate the direction of increment of t.

Explanation

Given data:

Vector function is r(t)=t2i+t4j+t6k .

Definition:

Consider a vector function as r(t)=f(t)i+g(t)j+h(t)k , then parametric equations to plot space curve C are,

x=f(t)y=g(t)z=h(t)

Here,

f(t) , g(t) , and h(t) are component functions of r, and

x, y, and z are parametric equations of C.

From definition, write the parametric equations of vector function r(t)=t2i+t4j+t6k .

x=t2

y=t4 (1)

z=t6 (2)

From parametric equations, it is obvious that, for any value of t when t≠0 the parametric equations are positive whereas, if t=0 the values of parametric equations are equal to zero

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Sect-13.1 P-1ESect-13.1 P-2ESect-13.1 P-3ESect-13.1 P-4ESect-13.1 P-5ESect-13.1 P-6ESect-13.1 P-7ESect-13.1 P-8ESect-13.1 P-9ESect-13.1 P-10E
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