Chapter 5: Q 7. (page 495)
Double-angle identities: Use double-angle identities to rewrite each of the following trigonometric expressions until no exponents are involved.
Chapter 5: Q 7. (page 495)
Double-angle identities: Use double-angle identities to rewrite each of the following trigonometric expressions until no exponents are involved.
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Get started for freeSolve 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.
True/False: Determinewhethereachofthestatementsthat follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.
(a) True or False: is a proper rational function.
(b) True or False: Every improper rational function can be expressed as the sum of a polynomial and a proper rational function.
(c) True or False: After polynomial long division of p(x) by q(x), the remainder r(x) has a degree strictly less than the degree of q(x).
(d) True or False: Polynomial long division can be used to divide two polynomials of the same degree.
(e) True or False: If a rational function is improper, then polynomial long division must be applied before using the method of partial fractions.
(f) True or False: The partial-fraction decomposition of is of the form
(g) True or False: The partial-fraction decomposition of is of the form .
(h) True or False: Every quadratic function can be written in the form
For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
Explain how to know when to use the trigonometric substitutions , Describe the trigonometric identity and the triangle that will be needed in each case. What are the possible values for and in each case?
For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
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