Math 2414 DHW 1
pdf
keyboard_arrow_up
School
University of Texas, Dallas *
*We aren’t endorsed by this school
Course
2413
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
4
Uploaded by DoctorLightning3936
Ashwin Indurti
Math2414SP24
Assignment DHW
1
–
Review
–
S24 due 01/22/2024 at 11:59pm CST
Problem 1.
(1 point)
Evaluate the limit, if it exists.
Enter ”infinity”, ”-infinity”, or
”DNE” if appropriate.
lim
x
→
2
x
4
-
16
x
-
2
=
Answer(s) submitted:
•
32
(correct)
Correct Answers:
•
32
Problem 2.
(1 point)
Evaluate the limit, if it exists.
Enter ”infinity”, ”-infinity”, or
”DNE” if appropriate.
lim
x
→
12
√
x
+
4
-
4
x
-
12
=
Answer(s) submitted:
•
1/8
(correct)
Correct Answers:
•
1/8
Problem 3.
(1 point)
Evaluate the limit, if it exists.
Enter ”infinity”, ”-infinity”, or
”DNE” if appropriate.
lim
b
→
7
1
b
-
1
7
b
-
7
=
Answer(s) submitted:
•
-1/49
(correct)
Correct Answers:
•
-1/49
Problem 4.
(1 point)
Evaluate the limit, if it exists.
Enter ”infinity”, ”-infinity”, or
”DNE” if appropriate.
(a) lim
x
→
3
-
1
x
3
-
27
=
(b) lim
x
→
3
+
1
x
3
-
27
=
Answer(s) submitted:
•
-infinity
•
infinity
(correct)
Correct Answers:
•
-infinity
•
infinity
Problem 5.
(1 point)
Evaluate the limit, if it exists.
Enter ”infinity”, ”-infinity”, or
”DNE” if appropriate.
lim
x
→
8
+
x
-
5
x
2
(
x
-
8
)
=
Answer(s) submitted:
•
infinity
(correct)
Correct Answers:
•
infinity
Problem 6.
(1 point)
Evaluate the limit, if it exists.
Enter ”infinity”, ”-infinity”, or
”DNE” if appropriate.
lim
x
→
3
-
x
2
-
9
x
+
18
x
2
-
6
x
+
9
=
Answer(s) submitted:
•
infinity
(correct)
Correct Answers:
•
infinity
Problem 7.
(1 point)
Evaluate the limit, if it exists.
Enter ”infinity”, ”-infinity”, or
”DNE” if appropriate.
lim
x
→
∞
tan
-
1
(
x
6
-
x
8
) =
Answer(s) submitted:
•
-pi/2
(correct)
Correct Answers:
•
-pi/2
1
Problem 8.
(1 point)
Evaluate the limit, if it exists.
Enter ”infinity”, ”-infinity”, or
”DNE” if appropriate.
(a) lim
x
→
∞
√
3
+
8
x
2
11
+
9
x
=
(b)
lim
x
→-
∞
√
3
+
8
x
2
11
+
9
x
=
Answer(s) submitted:
•
(sqrt8)/9
•
-(sqrt8)/9
(correct)
Correct Answers:
•
[sqrt(8)]/9
•
-sqrt(8)/9
Problem 9.
(1 point)
Evaluate the limit, if it exists.
Enter ”infinity”, ”-infinity”, or
”DNE” if appropriate.
lim
x
→
∞
x
4
-
2
x
2
+
5
x
5
+
3
x
3
=
Answer(s) submitted:
•
0
(correct)
Correct Answers:
•
0
Problem 10.
(1 point)
Evaluate the limit, if it exists.
Enter ”infinity”, ”-infinity”, or
”DNE” if appropriate.
lim
x
→-
∞
5
x
3
+
x
-
3
3
x
2
-
5
x
+
3
=
Answer(s) submitted:
•
-infinity
(correct)
Correct Answers:
•
-infinity
Problem 11.
(1 point)
Evaluate the limit, if it exists.
Enter ”infinity”, ”-infinity”, or
”DNE” if appropriate.
lim
x
→
0
+
ln
8
x
2
=
Answer(s) submitted:
•
infinity
(correct)
Correct Answers:
•
infinity
Problem 12.
(1 point)
Evaluate the limit, if it exists.
Enter ”infinity”, ”-infinity”, or
”DNE” if appropriate.
lim
x
→
∞
3
e
x
+
2
e
-
x
9
e
x
-
3
e
-
x
=
Answer(s) submitted:
•
1/3
(correct)
Correct Answers:
•
1/3
Problem 13.
(1 point)
Evaluate the limit, if it exists.
Enter ”infinity”, ”-infinity”, or
”DNE” if appropriate.
lim
x
→
∞
5
x
-
5ln
x
=
Answer(s) submitted:
•
infinity
(correct)
Correct Answers:
•
infinity
Problem 14.
(1 point)
Evaluate the limit, if it exists.
Enter ”infinity”, ”-infinity”, or
”DNE” if appropriate.
lim
x
→
1
7
ln
x
-
7
x
-
1
=
Answer(s) submitted:
•
7/2
(correct)
Correct Answers:
•
7/2
Problem 15.
(1 point)
Evaluate the limit, if it exists.
Enter ”infinity”, ”-infinity”, or
”DNE” if appropriate.
lim
x
→
0
+
5
√
x
ln
(
x
) =
Answer(s) submitted:
•
0
(correct)
Correct Answers:
•
0
2
Problem 16.
(1 point)
Evaluate the limit, if it exists.
Enter ”infinity”, ”-infinity”, or
”DNE” if appropriate.
lim
x
→
∞
3
p
x
2
+
2
x
-
3
x
=
Answer(s) submitted:
•
3
(correct)
Correct Answers:
•
3/1
Problem 17.
(1 point)
Differentiate
f
(
x
) =
x
3
tan
-
1
(
2
x
)
. (Note: You can enter ”arctan”
or ”tan
(
-
1
)
”
fortheinversetangent
.
)
f
0
(
x
) =
Answer(s) submitted:
•
((2xˆ3)/(1+4xˆ2)) + (3xˆ2arctan(2x))
(correct)
Correct Answers:
•
3*xˆ2*atan(2*x)+xˆ3*2/(1+4*xˆ2)
Problem 18.
(1 point)
Differentiate
f
(
x
) =
8arctan
(
5sin
(
2
x
))
.
f
0
(
x
) =
Answer(s) submitted:
•
(8/(1+(5sin(2x))ˆ2))*(5cos(2x))*2
(correct)
Correct Answers:
•
8*5*2*cos(2*x)/(1+5*5*(sin(2*x))**2)
Problem 19.
(1 point)
Differentiate
y
=
-
4
x
sin
1
x
.
y
0
=
Answer(s) submitted:
•
(-4sin(1/x))+((-4x)(-cos(1/x))/(xx))
(correct)
Correct Answers:
•
(-4)* (sin(1/x) -(1/x)cos(1/x))
Problem 20.
(1 point)
Suppose that
f
(
x
) =
2
x
2
√
5
x
2
+
2
.
Find
f
0
(
x
)
, and then evaluate
f
0
at
x
=
1 and
x
=
-
2.
(Enter
”sqrt(...)” for square roots, or ”(...)
(
3
/
2
)
”
forpowerso froots
.
)
f
0
(
1
)
=
f
0
(
-
2
)
=
Answer(s) submitted:
•
((4sqrt7)-10/(sqrt7))/7
•
((-8sqrt22)-(-80/(sqrt22)))/22
(correct)
Correct Answers:
•
18/[7ˆ(3/2)]
•
-96/[22ˆ(3/2)]
Problem 21.
(1 point)
Given
f
(
x
) =
e
-
2
x
cos2
x
, find the slope-intercept form of the
equation of the line tangent to the curve at the point when
x
=
0.
y
=
Answer(s) submitted:
•
-2x+1
(correct)
Correct Answers:
•
-(2)x + 1
3
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Problem 22.
(1 point)
Let
f
(
x
) =
x
3
-
15
x
2
+
63
x
+
4. Find the open intervals on which
f
is increasing, and the intervals on which
f
is decreasing. Then
find all values of
x
corresponding to local extrema.
1.
f
is increasing on the intervals
2.
f
is decreasing on the intervals
3.
The local maxima of
f
occur at
x
=
4.
The local minima of
f
occur at
x
=
Notes:
In the first two, your answer should either be a single in-
terval, such as (0,1), a comma separated list of intervals, such as
(-inf, 2), (3,4), or the word “none”.
In the last two, your answer should be a comma separated list of
x
values or the word “none”.
Answer(s) submitted:
•
(-inf,3),(7,inf)
•
(3,7)
•
3
•
7
(correct)
Correct Answers:
•
(-infinity,3), (7,infinity)
•
(3,7)
•
3
•
7
Generated by c WeBWorK, http://webwork.maa.org, Mathematical Association of America
4