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# To construct the snowflake curve, start with an

ISBN: 9781285740621 127

## Solution for problem 5 Chapter 11

Calculus | 8th Edition

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Calculus | 8th Edition

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11
5
Problem 5

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 after step n of the construction), respectively. Find formulas for sn, ln, and pn. (b) Show that pn l ` as n l `. (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.

Step-by-Step Solution:
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##### ISBN: 9781285740621

This full solution covers the following key subjects: curve, snowflake, SIDE, length, show. This expansive textbook survival guide covers 16 chapters, and 250 solutions. The full step-by-step solution to problem: 5 from chapter: 11 was answered by , our top Calculus solution expert on 11/10/17, 05:27PM. This textbook survival guide was created for the textbook: Calculus, edition: 8. Calculus was written by and is associated to the ISBN: 9781285740621. The answer to “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 after step n of the construction), respectively. Find formulas for sn, ln, and pn. (b) Show that pn l ` as n l `. (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.” is broken down into a number of easy to follow steps, and 166 words. Since the solution to 5 from 11 chapter was answered, more than 234 students have viewed the full step-by-step answer.

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