Chapter 5: Q. 12 (page 478)
What, if anything, does the divergence of and the comparison test tell you about the convergence or divergence of and why?
Short Answer
The convergence of and comparison test are useful to tell the convergence of .
Chapter 5: Q. 12 (page 478)
What, if anything, does the divergence of and the comparison test tell you about the convergence or divergence of and why?
The convergence of and comparison test are useful to tell the convergence of .
All the tools & learning materials you need for study success - in one app.
Get started for freeComplete the square for each quadratic in Exercises 28–33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.
For each integral in Exercises 5–8, write down three integrals that will have that form after a substitution of variables.
Solve the integral:
True/False: Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.
(a) True or False: The substitution x = 2 sec u is a suitable choice for solving.
(b) True or False: The substitution x = 2 sec u is a suitable choice for solving.
(c) True or False: The substitution x = 2 tan u is a suitable choice for solving
(d) True or False: The substitution x = 2 sin u is a suitable choice for solving
(e) True or False: Trigonometric substitution is a useful strategy for solving any integral that involves an expression of the form .
(f) True or False: Trigonometric substitution doesn’t solve an integral; rather, it helps you rewrite integrals as ones that are easier to solve by other methods.
(g) True or False: When using trigonometric substitution with , we must consider the cases and separately.
(h) True or False: When using trigonometric substitution with , we must consider the cases and separately.
Solvethe following two ways:
(a) with the substitution
(b) with the trigonometric substitution x = 2 tan u.
What do you think about this solution?
We value your feedback to improve our textbook solutions.