(a)
To Find: The formula for
(a)
Answer to Problem 3P
The required formula is
Explanation of Solution
Given:
The given diagram is shown in Figure 1
Figure 1
Calculation:
Consider the table shown in Table 1
Table 1
Consider the stage each side is replaced by the shorter sides each of the length of
Thus, the required formula is
(b)
To Prove: The value
(b)
Explanation of Solution
Calculation:
Consider the formula for
Since,
Hence, proved.
(c)
To Find: The sum of the infinite series to find the area enclosed by the snow flake curve.
(c)
Answer to Problem 3P
The area enclosed by the snowflake is
Explanation of Solution
Calculation:
The area of each of the small triangles added at the given stage is one fourth of the area of the triangle added at the preceding stage. Consider the area of the original triangle and then, the area
Since, the small triangle is added to the sides at every stage so it follow that the area is added to the figure of the next stage as,
Then, the total area is of the form,
Then, the area of the original equilateral triangle with sides is,
Thus, the area of the enclosed by the snowflake curve is,
Chapter 8 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning