Chapter 5: Q.1TB (page 477)
Solve the limit \(\lim_{x\rightarrow \infty}x^{-\frac{2}{3}}\).
Short Answer
\(0\)
Chapter 5: Q.1TB (page 477)
Solve the limit \(\lim_{x\rightarrow \infty}x^{-\frac{2}{3}}\).
\(0\)
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Get started for freeConsider the integral .
(a) Solve this integral by using u-substitution.
(b) Solve the integral another way, using algebra to multiply out the integrand first.
(c) How must your two answers be related? Use algebra to prove this relationship.
Solve each of the integrals in Exercises 39โ74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.
Solve given definite 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 doesnโt 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.
Complete the square for each quadratic in Exercises 28โ33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.
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