30/12/2019 Homework 3
Dashboard / MATH 1013 2019 Fall / 9 September - 15 September / Homework 3
Started on Friday, 13 September 2019, 3:37 PM
State Finished
Completed on Friday, 13 September 2019, 4:09 PM
Time taken 32 mins 6 secs
Grade 100.00 out of 100.00
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30/12/2019 Homework 3
Question 1
Use the given graphs of the function f (left, in blue) and g
Correct
Mark 5.00 out of
(right, in red) to find the following limits:
5.00
1. lim [f (x) + g(x)] = DNE help (limits)
x→1
2. lim [f (x) + g(x)] = 0
x→2
3. lim f (x)g(x) = 0
x→0
f (x)
4. lim = 0
x→0 g(x)
5. lim √3 + f (x) = sqrt(2)
x→−1
Note: You can click on the graphs to enlarge the images.
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30/12/2019 Homework 3
Results for this submission
Answer
# Entered Correct Answer
Preview
1 DNE DNE DNE
2 0 0 1 + −1 + 1 − 1
3 0 0 0
4 0 0 0
5 1.41421 √2 √3 − 1
All of the answers above are correct.
Question 2
Evaluate the limit
Correct
Mark 5.00 out of 2
x − 7x + 6
5.00
lim
2
x→1 x − 5x + 4
Enter I for ∞, -I for −∞, and DNE if the limit does not exist.
Limit = 5/3
Results for this submission
Answer
# Entered Correct Answer
Preview
5
1 1.66666666666667 1.66666666666667
3
The answer above is correct.
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30/12/2019 Homework 3
Question 3 2
x − 81
Correct Evaluate the limit: lim = 108
x→9
Mark 5.00 out of √x − 3
5.00
help (limits)
Results for this submission
# Entered Answer Preview Correct Answer
1 108 108 108
The answer above is correct.
Question 4
Evaluate the limit:
Correct
2 1
Mark 5.00 out of lim ( − ) = -1/8 help
5.00 t→0 t
t √4 + t
(limits)
Results for this submission
# Entered Answer Preview Correct Answer
−1 −1
1 -0.125
8 8
The answer above is correct.
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30/12/2019 Homework 3
Question 5
Evaluate the following limits:
Correct
Mark 5.00 out of 2
5.00 1. lim = infinity
6
x→5 (x − 5)
1
2. lim = -infinity
2
x→−7
−
x (x + 7)
2
3. lim = -infinity
3
x→5
−
(x − 5)
2
4. lim = infinity
x→3
+
x − 3
Use "infinity" for "∞" and "-infinity" for "−∞".
Results for this submission
# Entered Answer Preview Correct Answer
1 infinity ∞ ∞
2 -infinity −∞ −∞
3 -infinity −∞ −∞
4 infinity ∞ ∞
All of the answers above are correct.
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30/12/2019 Homework 3
Question 6
Evaluate the following limits. If needed, enter INF for ∞ and
Correct
Mark 6.00 out of
MINF for −∞.
6.00
(a)
2
lim (√x − 2x + 1 − x) =
x→∞
-1
The corresponding horizontal asymptote has equation
y = -1
(Type in DNE if there is no corresponding horizontal
asymptote.)
(b)
2
lim (√ x − 2x + 1 − x) =
x→−∞
INF
The corresponding horizontal asymptote has equation
y = DNE
(Type in DNE if there is no corresponding horizontal
asymptote.)
Results for this submission
# Entered Answer Preview Correct Answer
1 -1 −1 −1
2 -1 −1 −1
3 INF INF INF
4 DNE DNE DNE
All of the answers above are correct.
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30/12/2019 Homework 3
Question 7
Evaluate
Correct
Mark 5.00 out of
5.00 √x4 + 4x3 − 8
lim
x→∞ 2
5x + 1
1/5
Results for this submission
# Entered Answer Preview Correct Answer
1
1 0.2 0.2
5
The answer above is correct.
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30/12/2019 Homework 3
Question 8
Using long division, you can calculate that
Correct
Mark 6.00 out of 3 2
2x − 10x + 7x − 22 R(x)
6.00
f (x) = = Q(x) + .
2 2
2x + 5 2x + 5
The quotient Q(x) is x-5 .
The remainder R(x) is 2x+3
.
From this you can conclude that y = f (x) has an oblique (or
slant) asymptote given by the line with equation y = Q(x)
R(x)
because lim
2
= 0 .
x→±∞ 2x + 5
Results for this submission
# Entered Answer Preview Correct Answer
1 x-5 x − 5 x − 5
2 2*x+3 2x + 3 2x + 3
3 Q(X) Q(X) Q(X)
4 0 0 0
All of the answers above are correct.
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30/12/2019 Homework 3
Question 9
If
Correct
Mark 5.00 out of 2
5.00 1x − 4 ≤ f (x) ≤ x − 5x + 5
determine lim f (x) = -1
x→3
What theorem did you use to arrive at your answer?
Sandwich theorem
Results for this submission
# Entered Answer Preview Correct Answe
-1
1 -1 -1
Sand
wich
2 theo Sandwich theorem The Squeeze Th
rem
All of the answers above are correct.
Question 10
Find the following limit. If the limit goes to ∞, write "inf". If a
Correct
Mark 5.00 out of
limit goes to −∞, write "-inf".
5.00
−3x
lim [e cos(3x)]
x→∞
Limit: 0
Results for this submission
# Entered Answer Preview Correct Answer
1 0 0 0
The answer above is correct.
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30/12/2019 Homework 3
Question 11
Are the following functions one-to-one?
Correct
Mark 5.00 out of
5.00 No 1. f (x) = x 2
+ 3
No 2. f (x) = |x − 4|
Yes 3. f (x) = 3x + 4
1
Yes 4. f (x) =
x
Results for this submission
# Entered Answer Preview Correct Answer
1 No No No
2 No No No
3 Yes Yes Yes
4 Yes Yes Yes
All of the answers above are correct.
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30/12/2019 Homework 3
Question 12
Suppose
Correct
Mark 6.00 out of
2x − 1
6.00
f (x) = .
3x − 1
Then
f
−1
(x) = (x-1)/(3x-2) .
Results for this submission
Answer Correct
# Entered
Preview Answer
(x-1)/(3*x- x − 1 x − 1
1
2) 3x − 2 3x − 2
The answer above is correct.
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30/12/2019 Homework 3
Question 13
Below is the graph of a function f :
Correct
Mark 5.00 out of
5.00
Graph A
Graph B
Graph C
The inverse of the function f is (A, B or C): A
Results for this submission
# Entered Answer Preview Correct Answer
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30/12/2019 Homework 3
1 A A A
The answer above is correct.
Question 14
Find (a) the domain of f , (b) f −1
, and (c) the domain of f −1
.
Correct
2x
f (x) = √3 − e
Mark 6.00 out of
6.00
(a) x ≤ ln(sqrt(3))
(b) f −1
(x) = ln(sqrt(3-x^2))
(c) 0 ≤ x < sqrt(3)
Results for this submission
# Entered Answer Preview Correct Answer
1 0.549306 ln(√3) 0.549306
ln(sqrt(3-
2 ln(√3 − x )
2
0.5 ln(3 − x )
2
(x^2)))
3 0 0 0
4 1.73205 √3 1.73205
All of the answers above are correct.
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30/12/2019 Homework 3
Question 15
Find the domain and the range of g(x) = sin −1
(3x + 1) .
Correct
Mark 5.00 out of
5.00
Domain: -2/3 ≤ x ≤ 0
Range: -pi/2 ≤ y ≤ pi/2
Results for this submission
Answer
# Entered Correct Answer
Preview
−2
1 -0.666666666666667 −0.66666666666
3
2 0 0 0
−π −π
3 -1.5708
2 2
π π
4 1.5708
2 2
All of the answers above are correct.
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30/12/2019 Homework 3
Question 16
Let F be the function below
Correct
Mark 5.00 out of
5.00
(Click on graph to enlarge)
Evaluate the following expressions.
Note: Enter 'DNE' if the limit does not exist or is not defined.
You can just write 'yes' or 'no' for the yes/no questions.
a) lim F (x) = 2 b) Is F (x) continuous at x = 1
x→1
no
c) lim F (x) = DNE d) Is F (x) continuous at x = 2
x→2
no
e) lim F (x) = 3 f) Is F (x) continuous at x = 3
x→3
no
Results for this submission
# Entered Answer Preview Correct Answer
1 2 2 2
2 NO NO NO
3 DNE DNE DNE
4 NO NO NO
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30/12/2019 Homework 3
5 3 3 3
6 NO NO NO
All of the answers above are correct.
Question 17
Find the values of c and d that make the function
Correct
Mark 6.00 out of
⎧ 5x if x < 1
6.00 ⎪
2
f (x) = ⎨ cx + d if 1 ≤ x < 2
⎩
⎪
6x if x ≥ 2
continuous.
c = 7/3
d = 8/3
Results for this submission
Answer
# Entered Correct Answer
Preview
7
1 2.33333333333333 2.33333333333333
3
8
2 2.66666666666667 2.66666666666667
3
All of the answers above are correct.
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30/12/2019 Homework 3
Question 18
Use continuity to evaluate
Correct
Mark 5.00 out of 2
4x − 16
5.00
lim arctan( )
2
x→2 3x − 6x
Enter I for ∞, -I for −∞, and DNE if the limit does not exist.
Use at least 4 decimals.
Limit = 1.212
Results for this submission
Answer
# Entered Correct Answer
Preview
1 1.212 1.212 1.21202565652432
The answer above is correct.
Question 19
Given the interval(s) on which the function is continuous.
Correct
Mark 5.00 out of 7x
5.00 f (x) = e − ln(x − 7)
NOTE: When using interval notation in WeBWorK,
remember that:
You use 'INF' for ∞ and '-INF' for −∞.
And use 'U' for the union symbol.
(7,INF)
Results for this submission
Answer Correct
# Entered
Preview Answer
1 (7,infinity) (7, ∞) (7, ∞)
The answer above is correct.
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30/12/2019 Homework 3
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