Chapter 11, Problem 5P
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Multivariable Calculus
8th Edition
James Stewart
ISBN: 9781305266643
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Chapter
Section
BuyFindarrow_forward
Multivariable Calculus
8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem
To construct the snowflake curve, start with an equilateral triangle with sides of length 1. Step 1 in the construction is to divide each side into three equal parts, construct an equilateral triangle on the middle part, and then delete the middle part (see the figure). Step 2 is to repeat step 1 for each side of the resulting polygon. This process is repeated at each succeeding step. The snowflake curve is the curve that results from repeating this process indefinitely.
- (a) Let sn, ln, and pn represent the number of sides, the length of a side, and the total length of the nth approximating curve (the curve obtained alter step n of the construction), respectively. Find formulas for sn, ln, and pn.
- (b) Show that pn → ∞ as n → ∞.
- (c) Sum an infinite series to find the area enclosed by the snowflake curve.
Note: Parts (b) and (c) show that the snowflake curve is infinitely long but encloses only a finite area.
FIGURE FOR PROBLEM 5
(a)
To determine
To find: The formula for the number of sides
Explanation
Calculation:
The equilateral triangle each of length,
Therefore the number of sides
In general the number of sides
The length of the side
(b)
To determine
To show: The total length of the
(c)
To determine
To find: The area enclosed by the snow flake curve.
Chapter 11 Solutions
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In the following table, the lengths of the sides of cubes are given. Determine the volumes of the cubes. Round ...
Mathematics For Machine Technology
The national highway Traffic Safety administration reported the percentage of traffic accidents occurring each ...
STATISTICS F/BUSINESS+ECONOMICS-TEXT
Write the equation for the graph of the function shown.
College Algebra (MindTap Course List)
In Exercise 17 and 18, use the following information: To determine what effect salespeople had on purchases, a ...
Mathematics: A Practical Odyssey
The Nielsen Home Technology Report provided information about home technology and its usage. The following data...
Statistics for Business & Economics, Revised (MindTap Course List)
According to the gamblers fallacy, if a coin toss results in heads three times in a row, then the probability o...
Research Methods for the Behavioral Sciences (MindTap Course List)
