THOMAS'CALCULUS EARLY TRANS. MYLABSPLUS
14th Edition
ISBN: 9780135420683
Author: Hass
Publisher: PEARSON
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Chapter 12.2, Problem 23E
(a)
To determine
Sketch the indicated
(b)
To determine
Sketch the indicated vector
(c)
To determine
Sketch the indicated vector
(d)
To determine
Sketch the indicated vector
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Students have asked these similar questions
Is the function f(x) continuous at x = 1?
(x)
7
6
5
4
3
2
1
0
-10 -9
-8 -7
-6
-5
-4
-3
-2
-1 0
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-71
Select the correct answer below:
The function f(x) is continuous at x = 1.
The right limit does not equal the left limit. Therefore, the function is not continuous.
The function f(x) is discontinuous at x = 1.
We cannot tell if the function is continuous or discontinuous.
Question
Is the function f(x) shown in the graph below continuous at x = -5?
f(z)
7
6
5
4
2
1
0
-10
-6 -5
-4
1
0
2
3
5
7
10
-1
-2
-3
-4
-5
Select the correct answer below:
The function f(x) is continuous.
The right limit exists. Therefore, the function is continuous.
The left limit exists. Therefore, the function is continuous.
The function f(x) is discontinuous.
We cannot tell if the function is continuous or discontinuous.
The graph of f(x) is given below. Select all of the true statements about the continuity of f(x) at x = -1.
654
-2-
-7-6-5-4-
2-1
1 2
5 6 7
02.
Select all that apply:
☐ f(x) is not continuous at x = -1 because f(-1) is not defined.
☐ f(x) is not continuous at x = −1 because lim f(x) does not exist.
x-1
☐ f(x) is not continuous at x = −1 because lim ƒ(x) ‡ ƒ(−1).
☐ f(x) is continuous at x = -1
J-←台
Chapter 12 Solutions
THOMAS'CALCULUS EARLY TRANS. MYLABSPLUS
Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...
Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - Find the distance from the point (3, −4, 2) to...Ch. 12.1 - Find the distance from the point (−2, 1, 4) to...Ch. 12.1 - Find the distance from the point (4, 3, 0) to...Ch. 12.1 - Find the distance from the
x-axis to the plane z =...Ch. 12.1 - In Exercises 35–14, describe the given set with a...Ch. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - In Exercises 35–14, describe the given set with a...Ch. 12.1 - The set of points in space equidistant from the...Ch. 12.1 - Prob. 43ECh. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - Prob. 45ECh. 12.1 - Write inequalities to describe the sets in...Ch. 12.1 - Prob. 47ECh. 12.1 - Prob. 48ECh. 12.1 - Prob. 49ECh. 12.1 - Prob. 50ECh. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Prob. 52ECh. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Prob. 54ECh. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Prob. 56ECh. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find equations for the sphere whose centers and...Ch. 12.1 - Find equations for the sphere whose centers and...Ch. 12.1 - Find equations for the sphere whose centers and...Ch. 12.1 - Prob. 64ECh. 12.1 - Prob. 65ECh. 12.1 - Prob. 66ECh. 12.1 - Prob. 67ECh. 12.1 - Prob. 68ECh. 12.1 - Prob. 69ECh. 12.1 - Prob. 70ECh. 12.1 - Prob. 71ECh. 12.1 - Prob. 72ECh. 12.1 - Prob. 73ECh. 12.1 - Prob. 74ECh. 12.1 - Prob. 75ECh. 12.1 - Find all points that simultaneously lie 3 units...Ch. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - Prob. 2ECh. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - Prob. 4ECh. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - Prob. 6ECh. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.2 - In Exercises 9–16, find the component form of the...Ch. 12.2 - Prob. 11ECh. 12.2 - Prob. 12ECh. 12.2 - The unit vector that makes an angle θ = 2π/3 with...Ch. 12.2 - Prob. 14ECh. 12.2 - The unit vector obtained by rotating the vector ...Ch. 12.2 - The unit vector obtained by rotating the vector ...Ch. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - In Exercises 17–22, express each vector in the...Ch. 12.2 - Prob. 22ECh. 12.2 - In Exercises 23 and 24, copy vectors u, v, and w...Ch. 12.2 - In Exercises 23 and 24, copy vectors u, v, and w...Ch. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - Prob. 27ECh. 12.2 - In Exercises 25–30, express each vector as a...Ch. 12.2 - Prob. 29ECh. 12.2 - In Exercises 25–30, express each vector as a...Ch. 12.2 - Find the vectors whose lengths and directions are...Ch. 12.2 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - In Exercises 35–38, find a. the direction of and...Ch. 12.2 - Prob. 36ECh. 12.2 - In Exercises 35–38, find a. the direction of and...Ch. 12.2 - Prob. 38ECh. 12.2 - Prob. 39ECh. 12.2 - If = −7i + 3j + 8k and A is the point (−2, −3,...Ch. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Linear combination Let u = ⟨1, 2, 2 ⟩, v = ⟨ 1,...Ch. 12.2 - Velocity An airplane is flying in the direction...Ch. 12.2 - (Continuation of Example 8.) What speed and...Ch. 12.2 - Prob. 47ECh. 12.2 - Consider a 50-N weight suspended by two wires as...Ch. 12.2 - Consider a w-N weight suspended by two wires as...Ch. 12.2 - Consider a 25-N weight suspended by two wires as...Ch. 12.2 - Location A bird flies from its nest 5 km in the...Ch. 12.2 - Use similar triangles to find the coordinates of...Ch. 12.2 - Prob. 53ECh. 12.2 - Prob. 54ECh. 12.2 - Prob. 55ECh. 12.2 - Prob. 56ECh. 12.2 - Prob. 57ECh. 12.2 - Prob. 58ECh. 12.2 - Prob. 59ECh. 12.3 - Prob. 1ECh. 12.3 - 2. v = (3/5)i + (4/5)k, u = 5i + 12j
v · u, |v|,...Ch. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - 5. v = 5j – 3k, u = i + j + k
v · u, |v|, |u|
the...Ch. 12.3 - Prob. 6ECh. 12.3 - Prob. 7ECh. 12.3 -
v · u, | v |, | u |
the cosine of the angle...Ch. 12.3 - Find the angles between the vectors in Exercises...Ch. 12.3 - Prob. 10ECh. 12.3 - Prob. 11ECh. 12.3 - Prob. 12ECh. 12.3 - Prob. 13ECh. 12.3 - Rectangle Find the measures of the angles between...Ch. 12.3 - Direction angles and direction cosines The...Ch. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.3 - Prob. 19ECh. 12.3 - Prob. 20ECh. 12.3 - Prob. 21ECh. 12.3 - Prob. 22ECh. 12.3 - When parallelograms are rectangles Prove that a...Ch. 12.3 - Prob. 24ECh. 12.3 - Prob. 25ECh. 12.3 - Prob. 26ECh. 12.3 - Prob. 27ECh. 12.3 - Prob. 28ECh. 12.3 - Prob. 29ECh. 12.3 - Prob. 30ECh. 12.3 - Prob. 31ECh. 12.3 - Prob. 32ECh. 12.3 - Prob. 33ECh. 12.3 - Prob. 34ECh. 12.3 - Prob. 35ECh. 12.3 - Prob. 36ECh. 12.3 - Prob. 37ECh. 12.3 - Prob. 38ECh. 12.3 - Prob. 39ECh. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Prob. 42ECh. 12.3 - Prob. 43ECh. 12.3 - Prob. 44ECh. 12.3 - Prob. 45ECh. 12.3 - Prob. 46ECh. 12.3 - Prob. 47ECh. 12.3 - Prob. 48ECh. 12.3 - Prob. 49ECh. 12.3 - Prob. 50ECh. 12.3 - Prob. 51ECh. 12.3 - Prob. 52ECh. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 12.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 12.4 - Prob. 17ECh. 12.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 12.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 12.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 12.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 12.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - In Exercises 25 and 26, find the magnitude of the...Ch. 12.4 - In Exercises 25 and 26, find the magnitude of the...Ch. 12.4 - Which of the following are always true, and which...Ch. 12.4 - Which of the following are always true, and which...Ch. 12.4 - Given nonzero vectors u, v, and w, use dot product...Ch. 12.4 - Prob. 30ECh. 12.4 - Prob. 31ECh. 12.4 - Prob. 32ECh. 12.4 - Prob. 33ECh. 12.4 - Prob. 34ECh. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the triangles whose vertices are...Ch. 12.4 - Find the areas of the triangles whose vertices are...Ch. 12.4 - Find the areas of the triangles whose vertices are...Ch. 12.4 - Find the areas of the triangles whose vertices are...Ch. 12.4 - Find the areas of the triangles whose vertices are...Ch. 12.4 - Find the areas of the triangles whose vertices are...Ch. 12.4 - Find the areas of the triangles whose vertices are...Ch. 12.4 - Find the volume of a parallelepiped with one of...Ch. 12.4 - Triangle area Find a 2 × 2 determinant formula for...Ch. 12.4 - Triangle area Find a concise 3 × 3 determinant...Ch. 12.4 - Using the methods of Section 6.1, where volume is...Ch. 12.4 - Using the methods of Section 6.1, where volume is...Ch. 12.4 - Using the methods of Section 6.1, where volume is...Ch. 12.4 - Using the methods of Section 6.1, where volume is...Ch. 12.4 - In Exercises 55–57, determine whether the given...Ch. 12.4 - In Exercises 55–57, determine whether the given...Ch. 12.4 - Prob. 57ECh. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Prob. 7ECh. 12.5 - Prob. 8ECh. 12.5 - Prob. 9ECh. 12.5 - Prob. 10ECh. 12.5 - Prob. 11ECh. 12.5 - Prob. 12ECh. 12.5 - Prob. 13ECh. 12.5 - Prob. 14ECh. 12.5 - Prob. 15ECh. 12.5 - Prob. 16ECh. 12.5 - Prob. 17ECh. 12.5 - Prob. 18ECh. 12.5 - Prob. 19ECh. 12.5 - Prob. 20ECh. 12.5 - Prob. 21ECh. 12.5 - Find equations for the planes in Exercises...Ch. 12.5 - Planes
Find equations for the planes in Exercises...Ch. 12.5 - Prob. 24ECh. 12.5 - Prob. 25ECh. 12.5 - Prob. 26ECh. 12.5 - Prob. 27ECh. 12.5 - Prob. 28ECh. 12.5 - Prob. 29ECh. 12.5 - Prob. 30ECh. 12.5 - Prob. 31ECh. 12.5 - Prob. 32ECh. 12.5 - Prob. 33ECh. 12.5 - Prob. 34ECh. 12.5 - Prob. 35ECh. 12.5 - Prob. 36ECh. 12.5 - Prob. 37ECh. 12.5 - Prob. 38ECh. 12.5 - Prob. 39ECh. 12.5 - Prob. 40ECh. 12.5 - Prob. 41ECh. 12.5 - Prob. 42ECh. 12.5 - Prob. 43ECh. 12.5 - Prob. 44ECh. 12.5 - Prob. 45ECh. 12.5 - Prob. 46ECh. 12.5 - Prob. 47ECh. 12.5 - Prob. 48ECh. 12.5 - Prob. 49ECh. 12.5 - Prob. 50ECh. 12.5 - Prob. 51ECh. 12.5 - Prob. 52ECh. 12.5 - Prob. 53ECh. 12.5 - Prob. 54ECh. 12.5 - Prob. 55ECh. 12.5 - Prob. 56ECh. 12.5 - Prob. 57ECh. 12.5 - Prob. 58ECh. 12.5 - In Exercises 57–60, find the point in which the...Ch. 12.5 - Prob. 60ECh. 12.5 - Find parametrizations for the lines in which the...Ch. 12.5 - Find parametrizations for the lines in which the...Ch. 12.5 - Find parametrizations for the lines in which the...Ch. 12.5 - Prob. 64ECh. 12.5 - Prob. 65ECh. 12.5 - Prob. 66ECh. 12.5 - Prob. 67ECh. 12.5 - Prob. 68ECh. 12.5 - Prob. 69ECh. 12.5 - Prob. 70ECh. 12.5 - Prob. 71ECh. 12.5 - Prob. 72ECh. 12.5 - Prob. 73ECh. 12.5 - Prob. 74ECh. 12.5 - Prob. 75ECh. 12.5 - Prob. 76ECh. 12.5 - Prob. 77ECh. 12.5 - Prob. 78ECh. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - Prob. 9ECh. 12.6 - Prob. 10ECh. 12.6 - Prob. 11ECh. 12.6 - Prob. 12ECh. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises 13–44.
Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises 13–44.
Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises 13-44.
x2...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Prob. 31ECh. 12.6 - Prob. 32ECh. 12.6 - Prob. 33ECh. 12.6 - Prob. 34ECh. 12.6 - Prob. 35ECh. 12.6 - Prob. 36ECh. 12.6 - Prob. 37ECh. 12.6 - Prob. 38ECh. 12.6 - Prob. 39ECh. 12.6 - Prob. 40ECh. 12.6 - Prob. 41ECh. 12.6 - Prob. 42ECh. 12.6 - Prob. 43ECh. 12.6 - Prob. 44ECh. 12.6 - Express the area A of the cross-section cut from...Ch. 12.6 - Prob. 46ECh. 12.6 - Prob. 47ECh. 12.6 - Prob. 48ECh. 12.6 - Prob. 49ECh. 12.6 - Prob. 50ECh. 12.6 - Prob. 51ECh. 12.6 - Prob. 52ECh. 12 - Prob. 1GYRCh. 12 - Prob. 2GYRCh. 12 - Prob. 3GYRCh. 12 - Prob. 4GYRCh. 12 - Prob. 5GYRCh. 12 - Prob. 6GYRCh. 12 - Prob. 7GYRCh. 12 - Prob. 8GYRCh. 12 - Prob. 9GYRCh. 12 - Prob. 10GYRCh. 12 - Prob. 11GYRCh. 12 - How do you find the distance from a point to a...Ch. 12 - Prob. 13GYRCh. 12 - Prob. 14GYRCh. 12 - Prob. 15GYRCh. 12 - Prob. 16GYRCh. 12 - Prob. 17GYRCh. 12 - Prob. 1PECh. 12 - Prob. 2PECh. 12 - Prob. 3PECh. 12 - Prob. 4PECh. 12 - Prob. 5PECh. 12 - Prob. 6PECh. 12 - Prob. 7PECh. 12 - Prob. 8PECh. 12 - Prob. 9PECh. 12 - Prob. 10PECh. 12 - Prob. 11PECh. 12 - Prob. 12PECh. 12 - Prob. 13PECh. 12 - Prob. 14PECh. 12 - Prob. 15PECh. 12 - Prob. 16PECh. 12 - Prob. 17PECh. 12 - Prob. 18PECh. 12 - Prob. 19PECh. 12 - Prob. 20PECh. 12 - Prob. 21PECh. 12 - Prob. 22PECh. 12 - Prob. 23PECh. 12 - Prob. 24PECh. 12 - Prob. 25PECh. 12 - Prob. 26PECh. 12 - Prob. 27PECh. 12 - Prob. 28PECh. 12 - Prob. 29PECh. 12 - Prob. 30PECh. 12 - Prob. 31PECh. 12 - Prob. 32PECh. 12 - Prob. 33PECh. 12 - Prob. 34PECh. 12 - Prob. 35PECh. 12 - Prob. 36PECh. 12 - Prob. 37PECh. 12 - Prob. 38PECh. 12 - Prob. 39PECh. 12 - Prob. 40PECh. 12 - Prob. 41PECh. 12 - Prob. 42PECh. 12 - Prob. 43PECh. 12 - Prob. 44PECh. 12 - Prob. 45PECh. 12 - Prob. 46PECh. 12 - Prob. 47PECh. 12 - Prob. 48PECh. 12 - Prob. 49PECh. 12 - Prob. 50PECh. 12 - Prob. 51PECh. 12 - Prob. 52PECh. 12 - Prob. 53PECh. 12 - Prob. 54PECh. 12 - Prob. 55PECh. 12 - Prob. 56PECh. 12 - Prob. 57PECh. 12 - Prob. 58PECh. 12 - Prob. 59PECh. 12 - Prob. 60PECh. 12 - Prob. 61PECh. 12 - Prob. 62PECh. 12 - Prob. 63PECh. 12 - Prob. 64PECh. 12 - Prob. 65PECh. 12 - Prob. 66PECh. 12 - Prob. 67PECh. 12 - Prob. 68PECh. 12 - Prob. 69PECh. 12 - Prob. 70PECh. 12 - Prob. 71PECh. 12 - Prob. 72PECh. 12 - Prob. 73PECh. 12 - Prob. 74PECh. 12 - Prob. 75PECh. 12 - Prob. 76PECh. 12 - Prob. 1AAECh. 12 - Prob. 2AAECh. 12 - Prob. 3AAECh. 12 - Prob. 4AAECh. 12 - Prob. 5AAECh. 12 - Prob. 6AAECh. 12 - Prob. 7AAECh. 12 - Prob. 8AAECh. 12 - Prob. 9AAECh. 12 - Prob. 10AAECh. 12 - Prob. 11AAECh. 12 - Prob. 12AAECh. 12 - Prob. 13AAECh. 12 - Prob. 14AAECh. 12 - Prob. 15AAECh. 12 - Prob. 16AAECh. 12 - Prob. 17AAECh. 12 - Prob. 18AAECh. 12 - Prob. 19AAECh. 12 - Prob. 20AAECh. 12 - Prob. 21AAECh. 12 - Prob. 22AAECh. 12 - Prob. 23AAECh. 12 - Prob. 24AAECh. 12 - Prob. 25AAE
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- Let h(x, y, z) = — In (x) — z y7-4z - y4 + 3x²z — e²xy ln(z) + 10y²z. (a) Holding all other variables constant, take the partial derivative of h(x, y, z) with respect to x, 2 h(x, y, z). მ (b) Holding all other variables constant, take the partial derivative of h(x, y, z) with respect to y, 2 h(x, y, z).arrow_forwardints) A common representation of data uses matrices and vectors, so it is helpful to familiarize ourselves with linear algebra notation, as well as some simple operations. Define a vector ♬ to be a column vector. Then, the following properties hold: • cu with c some constant, is equal to a new vector where every element in cv is equal to the corresponding element in & multiplied by c. For example, 2 2 = ● √₁ + √2 is equal to a new vector with elements equal to the elementwise addition of ₁ and 2. For example, 問 2+4-6 = The above properties form our definition for a linear combination of vectors. √3 is a linear combination of √₁ and √2 if √3 = a√₁ + b√2, where a and b are some constants. Oftentimes, we stack column vectors to form a matrix. Define the column rank of a matrix A to be equal to the maximal number of linearly independent columns in A. A set of columns is linearly independent if no column can be written as a linear combination of any other column(s) within the set. If all…arrow_forwardThe graph of f(x) is given below. Select each true statement about the continuity of f(x) at x = 3. Select all that apply: 7 -6- 5 4 3 2 1- -7-6-5-4-3-2-1 1 2 3 4 5 6 7 +1 -2· 3. -4 -6- f(x) is not continuous at a = 3 because it is not defined at x = 3. ☐ f(x) is not continuous at a = - 3 because lim f(x) does not exist. 2-3 f(x) is not continuous at x = 3 because lim f(x) ‡ ƒ(3). →3 O f(x) is continuous at a = 3.arrow_forward
- Is the function f(x) continuous at x = 1? (z) 6 5 4 3. 2 1 0 -10 -9 -7 -5 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 Select the correct answer below: ○ The function f(x) is continuous at x = 1. ○ The right limit does not equal the left limit. Therefore, the function is not continuous. ○ The function f(x) is discontinuous at x = 1. ○ We cannot tell if the function is continuous or discontinuous.arrow_forwardIs the function f(x) shown in the graph below continuous at x = −5? f(x) 7 6 5 4 2 1 0 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 Select the correct answer below: The function f(x) is continuous. ○ The right limit exists. Therefore, the function is continuous. The left limit exists. Therefore, the function is continuous. The function f(x) is discontinuous. ○ We cannot tell if the function is continuous or discontinuous.arrow_forward4. Evaluate the following integrals. Show your work. a) -x b) f₁²x²/2 + x² dx c) fe³xdx d) [2 cos(5x) dx e) √ 35x6 3+5x7 dx 3 g) reve √ dt h) fx (x-5) 10 dx dt 1+12arrow_forward
- Math 2 question. thxarrow_forwardPlease help on this Math 1arrow_forward2. (5 points) Let f(x) = = - - - x² − 3x+7. Find the local minimum and maximum point(s) of f(x), and write them in the form (a, b), specifying whether each point is a minimum or maximum. Coordinates should be kept in fractions. Additionally, provide in your answer if f(x) has an absolute minimum or maximum over its entire domain with their corresponding values. Otherwise, state that there is no absolute maximum or minimum. As a reminder, ∞ and -∞ are not considered absolute maxima and minima respectively.arrow_forward
- Let h(x, y, z) = — In (x) — z y7-4z - y4 + 3x²z — e²xy ln(z) + 10y²z. (a) Holding all other variables constant, take the partial derivative of h(x, y, z) with respect to x, 2 h(x, y, z). მ (b) Holding all other variables constant, take the partial derivative of h(x, y, z) with respect to y, 2 h(x, y, z).arrow_forwardmath help plzarrow_forwardYou guys solved for the wrong answer. The answer in the box is incorrect help me solve for the right one.arrow_forward
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