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Chapter 5: Q. 4TB (page 463)

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.
$f (x) = \sin^{- 1} (\frac{x}{3})$

Short Answer

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Step 1. Given information.

given,

$f (x) = \sin^{- 1} (\frac{x}{3})$

Step 2.

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Most popular questions from this chapter

Solve $\int \frac{x^{2}}{1 + x^{2}} d x$ the following two ways:

(a) with the substitution $u = \tan^{- 1} x;$

(b) with the trigonometric substitution x = tan u.

Explain how to know when to use the trigonometric substitutions $x = a \sin u, x = a \tan u, a n d x = a \sec u$ , Describe the trigonometric identity and the triangle that will be needed in each case. What are the possible values for $x$ and $u$ in each case?

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: $f (x) = \frac{x + 1}{x - 1}$ 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 $\frac{x^{2} + 1}{x^{2} (x - 3)}$ is of the form $\frac{A}{x^{2}} + \frac{B}{x - 3}$

(g) True or False: The partial-fraction decomposition of $\frac{x^{2} + 1}{x^{2} (x - 3)}$ is of the form $\frac{B x + C}{x^{2}} + \frac{A}{x - 3}$ .

(h) True or False: Every quadratic function can be written in the form $A {(x - k)}^{2} + C$

Complete 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.

$2 x^{2} - 4 x + 1$

Solve the integral: $\int x \ln (x) d x$

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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.
$f (x) = \sin^{- 1} (\frac{x}{3})$

Short Answer

Step by step solution

Step 1. Given information.

Step 2.

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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. f(x)=sin−1⁡x3

Short Answer

Step by step solution

Step 1. Given information.

Step 2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Probability and Statistics

Discrete Mathematics

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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.
$f (x) = \sin^{- 1} (\frac{x}{3})$