Problem 3. (1 point) Problem 6. (1 point) Let f(x) = 1+x, ifx<3 7-x, if x 3 y Evaluate the following expressions. 5+ lim f(x) x-3- 4 3 lim f(x) x-3+ f(3) Is the function f continuous at 3? ? Answer(s) submitted: • 4 • 4 • 4 • Yes (correct) Problem 4. (1 point) Find values of x, if any, at which 2 2x f(x) = x-9 x+4 is not continuous (enter as comma separated list, smallest to largest). x= 2+ - དཀརར། + + + I 1 2 3 4 5 6 At each of the following points, choose the selection that best de- scribes the nature of the function's continuity there. ? 1. at x 1 ? 2. at x=4 ? 3. at x=3 Answer(s) submitted: • L • C • D Answer(s) submitted: -4, 9 (correct) Problem 5. (1 point) Find a value of the constant k, if possible, at which f(x) = is continuous everywhere. k = Skx² x<-3 7x+k x>-3 (enter "none" if no value). Answer(s) submitted: -21/8 (correct) (correct) Problem 7. (1 point) Carry out three steps of the Bisection Method for f(x) = 3* - x7 as follows: (a) Show that f(x) has a zero in [1,2]. (b) Determine which subinterval, [1,1.5] or [1.5,2], contains a zero. (c) Determine which interval, [1, 1.25], [1.25, 1.5], [1.5, 1.75], or [1.75,2], contains a zero. In part (b), the interval with a zero is In part (c), the interval with a zero is Answer(s) submitted: [1, 1.5] ⚫ [1, 1.25] (correct) 2 Problem 1. (1 point) Suppose that g is the function given by the graph below. Use the graph to fill in the blanks in the following sentences. Problem 2. (1 point) Use the given graph of the function g to find the following limits: g 3+ 2+ 16 2 -1 1 2 3 As x gets closer and closer to (but stays less than) 1, g(x) gets as close as we want to As x gets closer and closer to (but stays greater than) 1, g(x) gets as close as we want to As x gets closer and closer (but not equal) to 1, does g(x) get as close as we want to a single value? If such a value exists, enter it. If no such value exists, enter DNE. x= - Answer(s) submitted: • 3 • 2 • DNE (correct) 1. lim g(x) x-2- 2. lim g(x) x+2+ 3. lim g(x)= x→2 4. lim g(x) 5. g(2): = help (limits) Note: You can click on the graph to enlarge the image. Answer(s) submitted: • 2 • 0 • DNE • DNE • 1 (correct)
Problem 3. (1 point) Problem 6. (1 point) Let f(x) = 1+x, ifx<3 7-x, if x 3 y Evaluate the following expressions. 5+ lim f(x) x-3- 4 3 lim f(x) x-3+ f(3) Is the function f continuous at 3? ? Answer(s) submitted: • 4 • 4 • 4 • Yes (correct) Problem 4. (1 point) Find values of x, if any, at which 2 2x f(x) = x-9 x+4 is not continuous (enter as comma separated list, smallest to largest). x= 2+ - དཀརར། + + + I 1 2 3 4 5 6 At each of the following points, choose the selection that best de- scribes the nature of the function's continuity there. ? 1. at x 1 ? 2. at x=4 ? 3. at x=3 Answer(s) submitted: • L • C • D Answer(s) submitted: -4, 9 (correct) Problem 5. (1 point) Find a value of the constant k, if possible, at which f(x) = is continuous everywhere. k = Skx² x<-3 7x+k x>-3 (enter "none" if no value). Answer(s) submitted: -21/8 (correct) (correct) Problem 7. (1 point) Carry out three steps of the Bisection Method for f(x) = 3* - x7 as follows: (a) Show that f(x) has a zero in [1,2]. (b) Determine which subinterval, [1,1.5] or [1.5,2], contains a zero. (c) Determine which interval, [1, 1.25], [1.25, 1.5], [1.5, 1.75], or [1.75,2], contains a zero. In part (b), the interval with a zero is In part (c), the interval with a zero is Answer(s) submitted: [1, 1.5] ⚫ [1, 1.25] (correct) 2 Problem 1. (1 point) Suppose that g is the function given by the graph below. Use the graph to fill in the blanks in the following sentences. Problem 2. (1 point) Use the given graph of the function g to find the following limits: g 3+ 2+ 16 2 -1 1 2 3 As x gets closer and closer to (but stays less than) 1, g(x) gets as close as we want to As x gets closer and closer to (but stays greater than) 1, g(x) gets as close as we want to As x gets closer and closer (but not equal) to 1, does g(x) get as close as we want to a single value? If such a value exists, enter it. If no such value exists, enter DNE. x= - Answer(s) submitted: • 3 • 2 • DNE (correct) 1. lim g(x) x-2- 2. lim g(x) x+2+ 3. lim g(x)= x→2 4. lim g(x) 5. g(2): = help (limits) Note: You can click on the graph to enlarge the image. Answer(s) submitted: • 2 • 0 • DNE • DNE • 1 (correct)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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hello!
I do not understand continuity. I just finished learning the limits and continuity has been hard for me, I think i understand the concept but when there's exercises, i'm lost! I'm giving you questions with their answers. problem 3 is the most problematic. :(
Thank you.
Regards,
Hana
![Problem 3. (1 point)
Problem 6. (1 point)
Let
f(x) =
1+x,
ifx<3
7-x,
if x 3
y
Evaluate the following expressions.
5+
lim f(x)
x-3-
4
3
lim f(x)
x-3+
f(3)
Is the function f continuous at 3? ?
Answer(s) submitted:
• 4
• 4
• 4
• Yes
(correct)
Problem 4. (1 point)
Find values of x, if any, at which
2
2x
f(x) =
x-9
x+4
is not continuous (enter as comma separated list, smallest to
largest).
x=
2+
-
དཀརར།
+
+
+
I
1
2
3
4
5 6
At each of the following points, choose the selection that best de-
scribes the nature of the function's continuity there.
? 1. at x 1
? 2. at x=4
? 3. at x=3
Answer(s) submitted:
• L
• C
• D
Answer(s) submitted:
-4, 9
(correct)
Problem 5. (1 point)
Find a value of the constant k, if possible, at which
f(x)
=
is continuous everywhere.
k =
Skx²
x<-3
7x+k x>-3
(enter "none" if no value).
Answer(s) submitted:
-21/8
(correct)
(correct)
Problem 7. (1 point)
Carry out three steps of the Bisection Method for f(x) = 3* - x7
as follows:
(a) Show that f(x) has a zero in [1,2].
(b) Determine which subinterval, [1,1.5] or [1.5,2], contains a
zero.
(c) Determine which interval, [1, 1.25], [1.25, 1.5], [1.5, 1.75], or
[1.75,2], contains a zero.
In part (b), the interval with a zero is
In part (c), the interval with a zero is
Answer(s) submitted:
[1, 1.5]
⚫ [1, 1.25]
(correct)
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbcf0f621-50ee-41ce-bd9d-2f7ff8a381fe%2F88a63818-48d0-4198-b216-ba27ea1c4e54%2Fr31yhit_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 3. (1 point)
Problem 6. (1 point)
Let
f(x) =
1+x,
ifx<3
7-x,
if x 3
y
Evaluate the following expressions.
5+
lim f(x)
x-3-
4
3
lim f(x)
x-3+
f(3)
Is the function f continuous at 3? ?
Answer(s) submitted:
• 4
• 4
• 4
• Yes
(correct)
Problem 4. (1 point)
Find values of x, if any, at which
2
2x
f(x) =
x-9
x+4
is not continuous (enter as comma separated list, smallest to
largest).
x=
2+
-
དཀརར།
+
+
+
I
1
2
3
4
5 6
At each of the following points, choose the selection that best de-
scribes the nature of the function's continuity there.
? 1. at x 1
? 2. at x=4
? 3. at x=3
Answer(s) submitted:
• L
• C
• D
Answer(s) submitted:
-4, 9
(correct)
Problem 5. (1 point)
Find a value of the constant k, if possible, at which
f(x)
=
is continuous everywhere.
k =
Skx²
x<-3
7x+k x>-3
(enter "none" if no value).
Answer(s) submitted:
-21/8
(correct)
(correct)
Problem 7. (1 point)
Carry out three steps of the Bisection Method for f(x) = 3* - x7
as follows:
(a) Show that f(x) has a zero in [1,2].
(b) Determine which subinterval, [1,1.5] or [1.5,2], contains a
zero.
(c) Determine which interval, [1, 1.25], [1.25, 1.5], [1.5, 1.75], or
[1.75,2], contains a zero.
In part (b), the interval with a zero is
In part (c), the interval with a zero is
Answer(s) submitted:
[1, 1.5]
⚫ [1, 1.25]
(correct)
2
Transcribed Image Text:Problem 1. (1 point)
Suppose that g is the function given by the graph below. Use the
graph to fill in the blanks in the following sentences.
Problem 2. (1 point)
Use the given graph of the function g to find the following limits:
g
3+
2+
16
2
-1
1
2
3
As x gets closer and closer to (but stays less than) 1, g(x) gets as
close as we want to
As x gets closer and closer to (but stays greater than) 1, g(x) gets
as close as we want to
As x gets closer and closer (but not equal) to 1, does g(x) get as
close as we want to a single value? If such a value exists, enter it.
If no such value exists, enter DNE.
x= -
Answer(s) submitted:
• 3
• 2
• DNE
(correct)
1. lim g(x)
x-2-
2. lim g(x)
x+2+
3. lim g(x)=
x→2
4. lim g(x)
5. g(2):
=
help (limits)
Note: You can click on the graph to enlarge the image.
Answer(s) submitted:
• 2
• 0
• DNE
• DNE
• 1
(correct)
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