Continuous Extensions 41. Define g(3) in a way that extends g(x) = (x2-9)/(x continuous at x 3) to be Theory and Exa 55. A continuou and positive 3. 42. Define h(2) in a way that extends h(t) to be continuous at t 3t- 10)/(t 2) 2. one solution 43. Define f(1) in a way that extends f(s) = (s3-1)/(s - 1) to be continuous at s = 1 56. Explain wh 57. Roots of a three soluti 44. Define g(4) in a way that extends g(x) (x2 - 16)/(x2 3x 4) 58. A functio (x- b)2 + to be continuous at x 4. 45. For what value of a is 59. Solving a are values fax) =x- 1, x3 2ах, f(x) 60. Explain x 2 3 informatic continuous at every x? a. Find t 46. For what value of b is b. Find t Sx g(x)bx crosse x<-2 х, c. Find a d. Find continuous at every x? 1 у 3 47. For what values of a is e. Solve f(x)ax-2a 12, 61. Remova x z 2 that is co x< 2 removab continuous at every x? 48. For what values of b is 62. Nonren that is c x - b a nonre b1' g(x) 11 discont x2 +b, x > 0 63. A func continuous at every x? a. Use 49. For what values of a and b is co fun -2, x<-1 ix b, -1

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Continuous Extensions
41. Define g(3) in a way that extends g(x) = (x2-9)/(x
continuous at x
3) to be
Theory and Exa
55. A continuou
and positive
3.
42. Define h(2) in a way that extends h(t)
to be continuous at t
3t- 10)/(t 2)
2.
one solution
43. Define f(1) in a way that extends f(s) = (s3-1)/(s - 1) to be
continuous at s = 1
56. Explain wh
57. Roots of a
three soluti
44. Define g(4) in a way that extends
g(x) (x2 - 16)/(x2 3x 4)
58. A functio
(x- b)2
+
to be continuous at x
4.
45. For what value of a is
59. Solving a
are values
fax) =x- 1, x3
2ах,
f(x)
60. Explain
x 2 3
informatic
continuous at every x?
a. Find t
46. For what value of b is
b. Find t
Sx
g(x)bx
crosse
x<-2
х,
c. Find a
d. Find
continuous at every x?
1
у 3
47. For what values of a is
e. Solve
f(x)ax-2a
12,
61. Remova
x z 2
that is co
x< 2
removab
continuous at every x?
48. For what values of b is
62. Nonren
that is c
x - b
a nonre
b1'
g(x)
11
discont
x2 +b, x > 0
63. A func
continuous at every x?
a. Use
49. For what values of a and b is
co
fun
-2,
x<-1
ix b, -1<x< 1
f(x) =
3,
is
continuous at every x?
b. Is
50. For what values of a and b is
64. If fun
f(x)/
+3a-b, 0xs2
g(x) =
reaso
3x- 5,
x2
65. If the
continuous at every x?
must
answ
T In Exercises 51-54, graph the function f to see whether it appears to
have a continuous extension tox= 0.If it does, use Trace and Zoom
to find a good candidate for the extended function's value at x = 0,
66. Disc
0331
the
Transcribed Image Text:Continuous Extensions 41. Define g(3) in a way that extends g(x) = (x2-9)/(x continuous at x 3) to be Theory and Exa 55. A continuou and positive 3. 42. Define h(2) in a way that extends h(t) to be continuous at t 3t- 10)/(t 2) 2. one solution 43. Define f(1) in a way that extends f(s) = (s3-1)/(s - 1) to be continuous at s = 1 56. Explain wh 57. Roots of a three soluti 44. Define g(4) in a way that extends g(x) (x2 - 16)/(x2 3x 4) 58. A functio (x- b)2 + to be continuous at x 4. 45. For what value of a is 59. Solving a are values fax) =x- 1, x3 2ах, f(x) 60. Explain x 2 3 informatic continuous at every x? a. Find t 46. For what value of b is b. Find t Sx g(x)bx crosse x<-2 х, c. Find a d. Find continuous at every x? 1 у 3 47. For what values of a is e. Solve f(x)ax-2a 12, 61. Remova x z 2 that is co x< 2 removab continuous at every x? 48. For what values of b is 62. Nonren that is c x - b a nonre b1' g(x) 11 discont x2 +b, x > 0 63. A func continuous at every x? a. Use 49. For what values of a and b is co fun -2, x<-1 ix b, -1<x< 1 f(x) = 3, is continuous at every x? b. Is 50. For what values of a and b is 64. If fun f(x)/ +3a-b, 0xs2 g(x) = reaso 3x- 5, x2 65. If the continuous at every x? must answ T In Exercises 51-54, graph the function f to see whether it appears to have a continuous extension tox= 0.If it does, use Trace and Zoom to find a good candidate for the extended function's value at x = 0, 66. Disc 0331 the
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