Chapter 5: Q.10 (page 477)
Draw pictures to illustrate why the comparison test for improper integrals makes intuitive sense for both convergence comparisons and for divergence comparisons.
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Suppose you use polynomial long division to divide p(x) by q(x), and after doing your calculations you end up with the polynomial as the quotient above the top line, and the polynomial 3x − 1 at the bottom as the remainder. Then
Solve given definite integrals.
Solve the integral:.
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.
Domains and ranges of inverse trigonometric functions: For each function that follows, (a) list the domain and range, (b) sketch a labeled graph, and (c) discuss the domains and ranges in the context of the unit circle.
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