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 .
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For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
Solve given integrals by using polynomial long division to rewrite the integrand. This is one way that you can sometimes avoid using trigonometric substitution; moreover, sometimes it works when trigonometric substitution does not apply.
Consider the integral .
(a) Solve this integral by using u-substitution with and .
(b) Solve the integral another way, using u-substitution with and .
(c) How must your two answers be related? Use algebra to prove this relationship.
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