Suppose that g,(x) = 1/x' for x > 1, where r< 1. Let Drb denote the solid obtained by revolving the graph of g, on [1, b] about the x axis, and Sp, the surface area of D. On the one hand, we know that the surface area S1, of Gabriel's horn approaches o as b approaches o. On the other hand, we know from part (b) that the surface area S2, of D2 is no larger than 15 as b increases without bound. Is the surface area S,, of Drb bounded as a function of b, for each r with r > 1? Explain your answer.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
I want an anser of question number 1 - (c) and (d).
as u have answerd subpart a and b only.
![Suppose that g,(x) = 1/x' for x > 1, where r< 1. Let
Drb denote the solid obtained by revolving the graph
of g, on [1, b] about the x axis, and Sp, the surface area
of D. On the one hand, we know that the surface area
S1, of Gabriel's horn approaches o as b approaches o.
On the other hand, we know from part (b) that the
surface area S2, of D2 is no larger than 15 as b
increases without bound. Is the surface area S,, of Drb
bounded as a function of b, for each r with r > 1?
Explain your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1974f639-b7c8-43df-92b8-417d565eba23%2Fc3330d46-a2e2-44d5-8ea2-05bb240a29bb%2F0txplf.png&w=3840&q=75)
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