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23-24 How would you "remove the discontinuity" of f? In other words, how would you define f(2) in order to make f continuous at 2? x² - x - 2 +3 24. f(x) 23. f(x) = x² -4 x -2 25-32 Explain, using Theorems 4, 5, 7, and 9, why the function is continuous at every number in its domain. State the domain. 2x - x- 1 x2 + 1 25. F(x) : х 26. G(x) = .2 x + 1 2x2 - x-1 Vx – 2 3. 27. Q(x) = sin x 28. h(x) +3 x +1 U3R 29. h(x) = cos(1 – x²) tan x 30. В(х) V4 - x² 31. M(х) - 1+ 32. F(x) = sin(cos(sin.x)) EXEBCIZE2 33-34 Locate the discontinuities of the function and illustrate by graphing. 1 33. y = 1 + sin x 34. y = tan x 35-38 Use continuity to evaluate the limit 4 Theorem If f and g are continuous at a and if c is a constant, then the following functions are also continuous at a: 3. cf 2. f- g 1. f+g if g(a) # 0 4. fg 5. 5 Theorem a) Any polynomial is continuous everywhere; that is, it is continuc R=(-0, 0). b) Any rational function is continuous wherever it is defined; that uous on its domain. 7 Theorem The following types of functions are continuous at every numb their domains: • rational functions • polynomials • trigonometric functions • root functions so Limit Law 11 has now been proved. (We assume that the roots 9 Theorem If g is continuous at a and f is continuous at g(a), th posite function fog given by (f•g)(x) = f(g(x)) is continuous at %3D

23-24 How would you "remove the discontinuity" of f? In other words, how would you define f(2) in order to make f continuous at 2? x² - x - 2 +3 24. f(x) 23. f(x) = x² -4 x -2 25-32 Explain, using Theorems 4, 5, 7, and 9, why the function is continuous at every number in its domain. State the domain. 2x - x- 1 x2 + 1 25. F(x) : х 26. G(x) = .2 x + 1 2x2 - x-1 Vx – 2 3. 27. Q(x) = sin x 28. h(x) +3 x +1 U3R 29. h(x) = cos(1 – x²) tan x 30. В(х) V4 - x² 31. M(х) - 1+ 32. F(x) = sin(cos(sin.x)) EXEBCIZE2 33-34 Locate the discontinuities of the function and illustrate by graphing. 1 33. y = 1 + sin x 34. y = tan x 35-38 Use continuity to evaluate the limit 4 Theorem If f and g are continuous at a and if c is a constant, then the following functions are also continuous at a: 3. cf 2. f- g 1. f+g if g(a) # 0 4. fg 5. 5 Theorem a) Any polynomial is continuous everywhere; that is, it is continuc R=(-0, 0). b) Any rational function is continuous wherever it is defined; that uous on its domain. 7 Theorem The following types of functions are continuous at every numb their domains: • rational functions • polynomials • trigonometric functions • root functions so Limit Law 11 has now been proved. (We assume that the roots 9 Theorem If g is continuous at a and f is continuous at g(a), th posite function fog given by (f•g)(x) = f(g(x)) is continuous at %3D

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 18E
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23-24 How would you "remove the discontinuity" of f? In other words, how would you define f(2) in order to make f continuous at 2? x² - x - 2 +3 24. f(x) 23. f(x) = x² -4 x -2 25-32 Explain, using Theorems 4, 5, 7, and 9, why the function is continuous at every number in its domain. State the domain. 2x - x- 1 x2 + 1 25. F(x) : х 26. G(x) = .2 x + 1 2x2 - x-1 Vx – 2 3. 27. Q(x) = sin x 28. h(x) +3 x +1 U3R 29. h(x) = cos(1 – x²) tan x 30. В(х) V4 - x² 31. M(х) - 1+ 32. F(x) = sin(cos(sin.x)) EXEBCIZE2 33-34 Locate the discontinuities of the function and illustrate by graphing. 1 33. y = 1 + sin x 34. y = tan x 35-38 Use continuity to evaluate the limit
Transcribed Image Text:23-24 How would you "remove the discontinuity" of f? In other words, how would you define f(2) in order to make f continuous at 2? x² - x - 2 +3 24. f(x) 23. f(x) = x² -4 x -2 25-32 Explain, using Theorems 4, 5, 7, and 9, why the function is continuous at every number in its domain. State the domain. 2x - x- 1 x2 + 1 25. F(x) : х 26. G(x) = .2 x + 1 2x2 - x-1 Vx – 2 3. 27. Q(x) = sin x 28. h(x) +3 x +1 U3R 29. h(x) = cos(1 – x²) tan x 30. В(х) V4 - x² 31. M(х) - 1+ 32. F(x) = sin(cos(sin.x)) EXEBCIZE2 33-34 Locate the discontinuities of the function and illustrate by graphing. 1 33. y = 1 + sin x 34. y = tan x 35-38 Use continuity to evaluate the limit
4 Theorem If f and g are continuous at a and if c is a constant, then the following functions are also continuous at a: 3. cf 2. f- g 1. f+g if g(a) # 0 4. fg 5. 5 Theorem a) Any polynomial is continuous everywhere; that is, it is continuc R=(-0, 0). b) Any rational function is continuous wherever it is defined; that uous on its domain. 7 Theorem The following types of functions are continuous at every numb their domains: • rational functions • polynomials • trigonometric functions • root functions so Limit Law 11 has now been proved. (We assume that the roots 9 Theorem If g is continuous at a and f is continuous at g(a), th posite function fog given by (f•g)(x) = f(g(x)) is continuous at %3D
Transcribed Image Text:4 Theorem If f and g are continuous at a and if c is a constant, then the following functions are also continuous at a: 3. cf 2. f- g 1. f+g if g(a) # 0 4. fg 5. 5 Theorem a) Any polynomial is continuous everywhere; that is, it is continuc R=(-0, 0). b) Any rational function is continuous wherever it is defined; that uous on its domain. 7 Theorem The following types of functions are continuous at every numb their domains: • rational functions • polynomials • trigonometric functions • root functions so Limit Law 11 has now been proved. (We assume that the roots 9 Theorem If g is continuous at a and f is continuous at g(a), th posite function fog given by (f•g)(x) = f(g(x)) is continuous at %3D
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