Chapter 5: Q. 6 (page 441)
Describe two ways in which the long-division algorithm for polynomials is similar to the long-division algorithm for integers and then two ways in which the two algorithms are different.
The long division algorithm to divide polynomial is analogous to the long division algorithm for integers.
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Show that if , then , in the following two ways: (a) by using implicit differentiation, thinking of as a function of , and (b) by thinking of as a function of .
Solve given definite integral.
Consider the integral from the reading at the beginning of the section.
(a) Use the inverse trigonometric substitution to solve this integral.
(b) Use the trigonometric substitution to solve the integral.
(c) Compare and contrast the two methods used in parts (a) and (b).
Solve each of the integrals in Exercises 39–74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.
For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
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