Thomas' Calculus: Early Transcendentals, Single Variable (14th Edition)
14th Edition
ISBN: 9780134439419
Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher: PEARSON
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Chapter 12, Problem 25AAE
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DO these math problems without ai, show the solutions as well. and how you solved it. and could you do it with in the time spand
The Cartesian coordinates of a point are given.
(a) (-8, 8)
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(r.
= ([
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Chapter 12 Solutions
Thomas' Calculus: Early Transcendentals, Single Variable (14th Edition)
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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- 6. A particle moves according to a law of motion s(t) = t3-12t2 + 36t, where t is measured in seconds and s is in feet. (a) What is the velocity at time t? (b) What is the velocity after 3 s? (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (e) What is the acceleration at time t? (f) What is the acceleration after 3 s?arrow_forwardConstruct a table and find the indicated limit. √√x+2 If h(x) = then find lim h(x). X-8 X-8 Complete the table below. X 7.9 h(x) 7.99 7.999 8.001 8.01 8.1 (Type integers or decimals rounded to four decimal places as needed.)arrow_forwardUse the graph to find the following limits. (a) lim f(x) (b) lim f(x) X-1 x→1 (a) Find lim f(x) or state that it does not exist. Select the correct choice X-1 below and, if necessary, fill in the answer box within your choice. OA. lim f(x) = X-1 (Round to the nearest integer as needed.) OB. The limit does not exist. Qarrow_forward
- Officials in a certain region tend to raise the sales tax in years in which the state faces a budget deficit and then cut the tax when the state has a surplus. The graph shows the region's sales tax in recent years. Let T(x) represent the sales tax per dollar spent in year x. Find the desired limits and values, if they exist. Note that '01 represents 2001. Complete parts (a) through (e). Tax (in cents) T(X)4 8.5 8- OA. lim T(x)= cent(s) X-2007 (Type an integer or a decimal.) OB. The limit does not exist and is neither ∞ nor - ∞. Garrow_forwardDecide from the graph whether each limit exists. If a limit exists, estimate its value. (a) lim F(x) X➡-7 (b) lim F(x) X-2 (a) What is the value of the limit? Select the correct choice below and, if necessary, fill in the answer box within your choice. OA. lim F(x) = X-7 (Round to the nearest integer as needed.) OB. The limit does not exist. 17 Garrow_forwardFin lir X- a= (Us -10 OT Af(x) -10- 10arrow_forward
- Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist. f(x)=4x²+7x+1 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (Use a comma to separate answers as needed.) OA. f is discontinuous at the single value x = B. f is discontinuous at the single value x = OC. f is discontinuous at the two values x = OD. fis discontinuous at the two values x = OE. f is discontinuous at the two values x = The limit is The limit does not exist and is not co or - oo. The limit for the smaller value is The limit for the larger value is The limit for both values do not exist and are not co or - co. The limit for the smaller value does not exist and is not oo or - co. The limit for the larger value isarrow_forwardFind all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist. 8+x f(x) = x(x-1) (Use a comma to separate answers as needed.) OA. The function f is discontinuous at the single value x = OB. The function f is discontinuous at the single value x = OC. The function f is discontinuous at the two values x = OD. The function f is discontinuous at the two values x = not oo or -0. OE. The function f is discontinuous at the two values x = The limit is The limit does not exist and is not oo or - co. The limits for both values do not exist and are not co or - co. The limit for the smaller value is The limit for the larger value does not exist and is The limit for the smaller value does not exist and is not co or - co. The limit for the largerarrow_forwardi need help please . and please dont use chat gpt i am trying to learn and see the mistake i did when solving minearrow_forward
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