University Calculus: Early Transcendentals Plus MyLab Math -- Access Card Package (3rd Edition) (Integrated Review Courses in MyMathLab and MyStatLab)
3rd Edition
ISBN: 9780321999573
Author: Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.
Publisher: PEARSON
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Question
Chapter 11.6, Problem 52E
a.
To determine
Plot the given surface over the indicated domains.
b.
To determine
Plot the given surface over the indicated domains.
c.
To determine
Plot the given surface over the indicated domains.
d.
To determine
Plot the given surface over the indicated domains.
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(x)=2x-x2
2
a=2, b = 1/2, C=0
b) Vertex v
F(x)=ax 2 + bx + c
x=
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V=2.0L
YEF(- =) = 4
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JANUARY 17, 2025
WORKSHEET 1
Solve the following four problems on a separate sheet. Fully justify your answers to
MATH 122
ล
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earn full credit.
1. Let f(x) = 2x-
1x2
2
(a) Rewrite this quadratic function in standard form: f(x) = ax² + bx + c
and indicate the values of the coefficients: a, b and c.
(b) Find the vertex V, focus F, focal width, directrix D, and the axis of
symmetry for the graph of y = f(x).
(c) Plot a graph of y = f(x) and indicate all quantities found in part (b)
on your graph.
(d) Specify the domain and range of the function f.
OUR
2. Let g(x) = f(x) u(x) where f is the quadratic function from problem 1
and u is the unit step function:
u(x) = { 0
1 if x ≥0
0 if x<0
y = u(x)
0
(a) Write a piecewise formula for the function g.
(b) Sketch a graph of y = g(x).
(c) Indicate the domain and range of the function g.
X
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where u is the unit step function defined in problem 2.
3. Let…
Question 1
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Question 3: Construct the accessibility matrix Passociated with
the following graphs, and compute P2 and identify each at the
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P₂
Chapter 11 Solutions
University Calculus: Early Transcendentals Plus MyLab Math -- Access Card Package (3rd Edition) (Integrated Review Courses in MyMathLab and MyStatLab)
Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...
Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - Prob. 16ECh. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 35–14, describe the given set with a...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - In Exercises 35–14, describe the given set with a...Ch. 11.1 - The set of points in space equidistant from the...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - Prob. 34ECh. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - In Exercises 25–30, find the distance between...Ch. 11.1 - In Exercises 25–30, find the distance between...Ch. 11.1 - In Exercises 25–30, find the distance between...Ch. 11.1 - Prob. 44ECh. 11.1 - Prob. 45ECh. 11.1 - Prob. 46ECh. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find equations for the sphere whose centers and...Ch. 11.1 - Find equations for the sphere whose centers and...Ch. 11.1 - Prob. 53ECh. 11.1 - Prob. 54ECh. 11.1 - Prob. 55ECh. 11.1 - Prob. 56ECh. 11.1 - Prob. 57ECh. 11.1 - Prob. 58ECh. 11.1 - Find a formula for the distance from the point...Ch. 11.1 - Find a formula for the distance from the point...Ch. 11.1 - Find the perimeter of the triangle with vertices...Ch. 11.1 - Show that the point P(3, 1, 2) is equidistant from...Ch. 11.1 - Find an equation for the set of all points...Ch. 11.1 - Prob. 64ECh. 11.1 - Find the point on the sphere x2 + (y − 3)2 + (z +...Ch. 11.1 - Find the point equidistant from the points (0, 0,...Ch. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - Prob. 4ECh. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - Prob. 6ECh. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - In Exercises 9–16, find the component form of the...Ch. 11.2 - In Exercises 9–16, find the component form of the...Ch. 11.2 - In Exercises 9–16, find the component form of the...Ch. 11.2 - In Exercises 9–16, find the component form of the...Ch. 11.2 - The unit vector that makes an angle θ = 2π/3 with...Ch. 11.2 - The unit vector that makes an angle θ = −3π/4 with...Ch. 11.2 - The unit vector obtained by rotating the vector ...Ch. 11.2 - The unit vector obtained by rotating the vector ...Ch. 11.2 - In Exercises 17–22, express each vector in the...Ch. 11.2 - Prob. 18ECh. 11.2 - In Exercises 17–22, express each vector in the...Ch. 11.2 - In Exercises 17–22, express each vector in the...Ch. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - In Exercises 23 and 24, copy vectors u, v, and w...Ch. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - In Exercises 25–30, express each vector as a...Ch. 11.2 - Prob. 30ECh. 11.2 - Find the vectors whose lengths and directions are...Ch. 11.2 - Prob. 32ECh. 11.2 - Find a vector of magnitude 7 in the direction of v...Ch. 11.2 - Prob. 34ECh. 11.2 - In Exercises 35–38, find a. the direction of and...Ch. 11.2 - In Exercises 35–38, find a. the direction of and...Ch. 11.2 - In Exercises 35–38, find a. the direction of and...Ch. 11.2 - Prob. 38ECh. 11.2 - If = i + 4j − 2k and B is the point (5, 1, 3),...Ch. 11.2 - Prob. 40ECh. 11.2 - Linear combination Let u = 2i + j, v = i + j, and...Ch. 11.2 - Linear combination Let u = i − 2j, v = 2i + 3j,...Ch. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.2 - Consider a 100-N weight suspended by two wires as...Ch. 11.2 - Prob. 46ECh. 11.2 - Prob. 47ECh. 11.2 - Prob. 48ECh. 11.2 - Location A bird flies from its nest 5 km in the...Ch. 11.2 - Prob. 50ECh. 11.2 - Prob. 51ECh. 11.2 - Prob. 52ECh. 11.2 - Prob. 53ECh. 11.2 - Vectors are drawn from the center of a regular...Ch. 11.2 - Prob. 55ECh. 11.2 - Prob. 56ECh. 11.3 - Prob. 1ECh. 11.3 - 2. v = (3/5)i + (4/5)k, u = 5i + 12j
v · u, |v|,...Ch. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - 5. v = 5j – 3k, u = i + j + k
v · u, |v|, |u|
the...Ch. 11.3 - Prob. 6ECh. 11.3 - v = 5i + j,
v · u, | v |, | u |
the cosine of the...Ch. 11.3 -
v · u, | v |, | u |
the cosine of the angle...Ch. 11.3 - Find the angles between the vectors in Exercises...Ch. 11.3 - Find the angles between the vectors in Exercises...Ch. 11.3 - Find the angles between the vectors in Exercises...Ch. 11.3 - Find the angles between the vectors in Exercises...Ch. 11.3 - Prob. 13ECh. 11.3 - Rectangle Find the measures of the angles between...Ch. 11.3 - Direction angles and direction cosines The...Ch. 11.3 - Water main construction A water main is to be...Ch. 11.3 - Sums and differences In the accompanying figure,...Ch. 11.3 - Prob. 18ECh. 11.3 - Diagonals of a rhombus Show that the diagonals of...Ch. 11.3 - Perpendicular diagonals Show that squares are the...Ch. 11.3 - When parallelograms are rectangles Prove that a...Ch. 11.3 - Diagonal of parallelogram Show that the indicated...Ch. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Cauchy–Schwarz inequality Since u · v = |u| |v|...Ch. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Cancelation in dot products In real-number...Ch. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Prob. 32ECh. 11.3 - Prob. 33ECh. 11.3 - Prob. 34ECh. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Prob. 37ECh. 11.3 - Prob. 38ECh. 11.3 - Prob. 39ECh. 11.3 - Prob. 40ECh. 11.3 - Prob. 41ECh. 11.3 - Prob. 42ECh. 11.3 - Prob. 43ECh. 11.3 - Sailboat The wind passing over a boat’s sail...Ch. 11.3 -
Use this fact and the results of Exercise 33 or...Ch. 11.3 - Prob. 46ECh. 11.3 - Prob. 47ECh. 11.3 - Prob. 48ECh. 11.3 - Prob. 49ECh. 11.3 - Prob. 50ECh. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - Prob. 4ECh. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - Prob. 7ECh. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 11.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 11.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 11.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 11.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 11.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 11.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 11.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 11.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 11.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Which of the following are always true, and which...Ch. 11.4 - Which of the following are always true, and which...Ch. 11.4 - Given nonzero vectors u, v, and w, use dot product...Ch. 11.4 - Compute (i × j) × j and i × (j × j). What can you...Ch. 11.4 - Let u, v, and w be vectors. Which of the following...Ch. 11.4 - Prob. 32ECh. 11.4 - Cancelation in cross products If u × v = u × w and...Ch. 11.4 - Double cancelation If u ≠ 0 and if u × v = u × w...Ch. 11.4 - Find the areas of the parallelograms whose...Ch. 11.4 - Prob. 36ECh. 11.4 - Prob. 37ECh. 11.4 - Find the areas of the parallelograms whose...Ch. 11.4 - Find the areas of the parallelograms whose...Ch. 11.4 - Find the areas of the parallelograms whose...Ch. 11.4 - Find the areas of the triangles whose vertices are...Ch. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - Prob. 44ECh. 11.4 - Find the areas of the triangles whose vertices are...Ch. 11.4 - Prob. 46ECh. 11.4 - Find the areas of the triangles whose vertices are...Ch. 11.4 - Find the volume of a parallelepiped with one of...Ch. 11.4 - Triangle area Find a 2 × 2 determinant formula for...Ch. 11.4 - Triangle area Find a concise 3 × 3 determinant...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Prob. 7ECh. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Prob. 10ECh. 11.5 - Prob. 11ECh. 11.5 - Prob. 12ECh. 11.5 - Find parametrizations for the line segments...Ch. 11.5 - Prob. 14ECh. 11.5 - Find parametrizations for the line segments...Ch. 11.5 - Prob. 16ECh. 11.5 - Find parametrizations for the line segments...Ch. 11.5 - Find parametrizations for the line segments...Ch. 11.5 - Find parametrizations for the line segments...Ch. 11.5 - Prob. 20ECh. 11.5 - Find equations for the planes in Exercises...Ch. 11.5 - Find equations for the planes in Exercises...Ch. 11.5 - Planes
Find equations for the planes in Exercises...Ch. 11.5 - Planes
Find equations for the planes in Exercises...Ch. 11.5 - Find equations for the planes in Exercises...Ch. 11.5 - Find equations for the planes in Exercises...Ch. 11.5 - Prob. 27ECh. 11.5 - Prob. 28ECh. 11.5 - In Exercises 29 and 30, find the plane containing...Ch. 11.5 - In Exercises 29 and 30, find the plane containing...Ch. 11.5 - Prob. 31ECh. 11.5 - Prob. 32ECh. 11.5 - In Exercises 33–38, find the distance from the...Ch. 11.5 - In Exercises 33–38, find the distance from the...Ch. 11.5 - In Exercises 33–38, find the distance from the...Ch. 11.5 - In Exercises 33–38, find the distance from the...Ch. 11.5 - Prob. 37ECh. 11.5 - Prob. 38ECh. 11.5 - In Exercises 39–44, find the distance from the...Ch. 11.5 - In Exercises 39–44, find the distance from the...Ch. 11.5 - In Exercises 39–44, find the distance from the...Ch. 11.5 - In Exercises 39−44, find the distance from the...Ch. 11.5 - Prob. 43ECh. 11.5 - Prob. 44ECh. 11.5 - Find the distance from the plane x + 2y + 6z = 1...Ch. 11.5 - Find the distance from the line x = 2 + t, y = 1 +...Ch. 11.5 - Find the angles between the planes in Exercises 47...Ch. 11.5 - Prob. 48ECh. 11.5 - Prob. 49ECh. 11.5 - Prob. 50ECh. 11.5 - Prob. 51ECh. 11.5 - Prob. 52ECh. 11.5 - In Exercises 57–60, find the point in which the...Ch. 11.5 - In Exercises 57–60, find the point in which the...Ch. 11.5 - In Exercises 57–60, find the point in which the...Ch. 11.5 - Prob. 56ECh. 11.5 - Find parametrizations for the lines in which the...Ch. 11.5 - Prob. 58ECh. 11.5 - Prob. 59ECh. 11.5 - Prob. 60ECh. 11.5 - Given two lines in space, either they are...Ch. 11.5 - Given two lines in space, either they are...Ch. 11.5 - Use Equations (3) to generate a parametrization of...Ch. 11.5 - Use the component form to generate an equation for...Ch. 11.5 - Find the points in which the line x = 1 + 2t, y =...Ch. 11.5 - Find equations for the line in the plane z = 3...Ch. 11.5 - Prob. 67ECh. 11.5 - How can you tell when two planes A1x + B1y + C1z =...Ch. 11.5 - Find two different planes whose intersection is...Ch. 11.5 - Find a plane through the origin that is...Ch. 11.5 - The graph of is a plane for any nonzero numbers...Ch. 11.5 - Prob. 72ECh. 11.5 - Prob. 73ECh. 11.5 - Prob. 74ECh. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises 13–44.
Ch. 11.6 - Prob. 22ECh. 11.6 - Prob. 23ECh. 11.6 - Prob. 24ECh. 11.6 - Drawing
Sketch the surfaces in Exercises 13–44.
Ch. 11.6 - Prob. 26ECh. 11.6 - Prob. 27ECh. 11.6 - Prob. 28ECh. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Prob. 30ECh. 11.6 - Prob. 31ECh. 11.6 - Prob. 32ECh. 11.6 - Prob. 33ECh. 11.6 - Prob. 34ECh. 11.6 - Prob. 35ECh. 11.6 - Prob. 36ECh. 11.6 - Prob. 37ECh. 11.6 - Prob. 38ECh. 11.6 - Prob. 39ECh. 11.6 - Prob. 40ECh. 11.6 - Prob. 41ECh. 11.6 - Prob. 42ECh. 11.6 - Prob. 43ECh. 11.6 - Prob. 44ECh. 11.6 - Express the area A of the cross-section cut from...Ch. 11.6 - Prob. 46ECh. 11.6 - Prob. 47ECh. 11.6 - Prob. 48ECh. 11.6 - Prob. 49ECh. 11.6 - Prob. 50ECh. 11.6 - Prob. 51ECh. 11.6 - Prob. 52ECh. 11 - Prob. 1GYRCh. 11 - How are vectors added and subtracted...Ch. 11 - Prob. 3GYRCh. 11 - Prob. 4GYRCh. 11 - Define the dot product (scalar product) of two...Ch. 11 - Prob. 6GYRCh. 11 - Prob. 7GYRCh. 11 - Prob. 8GYRCh. 11 - Prob. 9GYRCh. 11 - Prob. 10GYRCh. 11 - Prob. 11GYRCh. 11 - Prob. 12GYRCh. 11 - What are box products? What significance do they...Ch. 11 - Prob. 14GYRCh. 11 - Prob. 15GYRCh. 11 - Prob. 16GYRCh. 11 - Prob. 17GYRCh. 11 - In Exercises 1–4, let u = ⟨−3, 4⟩ and v = ⟨2, −5⟩....Ch. 11 - Prob. 2PECh. 11 - Prob. 3PECh. 11 - Prob. 4PECh. 11 - Prob. 5PECh. 11 - In Exercises 5-8, find the component form of the...Ch. 11 - The vector 2 units long in the direction 4i − j
Ch. 11 - The vector 5 units long in the direction opposite...Ch. 11 - Express the vectors in Exercises 9–12 in terms of...Ch. 11 - Prob. 10PECh. 11 - Prob. 11PECh. 11 - Prob. 12PECh. 11 - Prob. 13PECh. 11 - Prob. 14PECh. 11 - Prob. 15PECh. 11 - Prob. 16PECh. 11 - In Exercises 17 and 18, find |v|, |u|, , the angle...Ch. 11 - Prob. 18PECh. 11 - In Exercises 19 and 20, find projv u.
v = 2i + j −...Ch. 11 - Prob. 20PECh. 11 - In Exercises 21 and 22, draw coordinate axes and...Ch. 11 - Prob. 22PECh. 11 - Prob. 23PECh. 11 - Prob. 24PECh. 11 - In Exercises 25 and 26, find (a) the area of the...Ch. 11 - Prob. 26PECh. 11 - Suppose that n is normal to a plane and that v is...Ch. 11 - Find a vector in the plane parallel to the line ax...Ch. 11 - In Exercises 29 and 30, find the distance from the...Ch. 11 - Prob. 30PECh. 11 - Prob. 31PECh. 11 - Parametrize the line segment joining the points...Ch. 11 - In Exercises 33 and 34, find the distance from the...Ch. 11 - Prob. 34PECh. 11 - Prob. 35PECh. 11 - Prob. 36PECh. 11 - In Exercises 37 and 38, find an equation for the...Ch. 11 - Prob. 38PECh. 11 - Prob. 39PECh. 11 - Prob. 40PECh. 11 - Find the acute angle between the planes x = 7 and...Ch. 11 - Prob. 42PECh. 11 - Find parametric equations for the line in which...Ch. 11 - Prob. 44PECh. 11 - Prob. 45PECh. 11 - Prob. 46PECh. 11 - Prob. 47PECh. 11 - Prob. 48PECh. 11 - Prob. 49PECh. 11 - Prob. 50PECh. 11 - Prob. 51PECh. 11 - Prob. 52PECh. 11 - Prob. 53PECh. 11 - Prob. 54PECh. 11 - Find the point in which the line through P(3, 2,...Ch. 11 - Prob. 56PECh. 11 - Prob. 57PECh. 11 - Prob. 58PECh. 11 - Prob. 59PECh. 11 - Is the line related in any way to the plane ?...Ch. 11 - Which of the following are equations for the plane...Ch. 11 - The parallelogram shown here has vertices at A(2,...Ch. 11 - Prob. 63PECh. 11 - Prob. 64PECh. 11 - Prob. 65PECh. 11 - Prob. 66PECh. 11 - Prob. 67PECh. 11 - Prob. 68PECh. 11 - Prob. 69PECh. 11 - Prob. 70PECh. 11 - Prob. 71PECh. 11 - Prob. 72PECh. 11 - Prob. 73PECh. 11 - Prob. 74PECh. 11 - Prob. 75PECh. 11 - Prob. 76PECh. 11 - Prob. 1AAECh. 11 - Prob. 2AAECh. 11 - Prob. 3AAECh. 11 - Prob. 4AAECh. 11 - Prob. 5AAECh. 11 - Prob. 6AAECh. 11 - Prob. 7AAECh. 11 - Prob. 8AAECh. 11 - Prob. 9AAECh. 11 - Prob. 10AAECh. 11 - Prob. 11AAECh. 11 - Prob. 12AAECh. 11 - Prob. 13AAECh. 11 - Prob. 14AAECh. 11 - Prob. 15AAECh. 11 - By forming the cross product of two appropriate...Ch. 11 - Prob. 17AAECh. 11 - Prob. 18AAE
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- Calculate these limits. If the limit is ∞ or -∞, write infinity or-infinity. If the limit does not exist, write DNE: Hint: Remember the first thing you check when you are looking at a limit of a quotient is the limit value of the denominator. 1. If the denominator does not go to 0, you should be able to right down the answer immediately. 2. If the denominator goes to 0, but the numerator does not, you will have to check the sign (±) of the quotient, from both sides if the limit is not one-sided. 3. If both the numerator and the denominator go to 0, you have to do the algebraic trick of rationalizing. So, group your limits into these three forms and work with them one group at a time. (a) lim t-pi/2 sint-√ sin 2t+14cos ² t 7 2 2 2cos t (b) lim sint + sin 2t+14cos = ∞ t-pi/2 2 2cos t (c) lim cost-√sin 2t+14cos² t = t-pi/2 2cos t (d) lim t→pi/2 cost+√ sin t + 14cos 2cos ² t = ∞ (e) lim sint-v sin 2 t + 14cos = 0 t-pi/2 (f) lim t-pi/2 sin t +√ sin 2sin 2 t 2 t + 14cos t 2sin t cost- (g)…arrow_forwardThink of this sheet of paper as the plane containing the vectors a = (1,1,0) and b = (2,0,0). Sketch the parallelogram P spanned by a and b. Which diagonal of P represents the vector a--b geometrically?arrow_forward(1) (14 points) Let a = (-2, 10, -4) and b = (3, 1, 1). (a) (4 points) Using the dot product determine the angle between a and b. (b) (2 points) Determine the cross product vector axb. (c) (4 points) Calculate the area of the parallelogram spanned by a and b. Justify your answer. 1arrow_forward
- (d) (4 points) Think of this sheet of paper as the plane containing the vectors a = (1,1,0) and b = (2,0,0). Sketch the parallelogram P spanned by a and b. Which diagonal of P represents the vector ab geometrically? d be .dx adjarrow_forward(2) (4 points) Find all vectors v having length 1 that are perpendicular to both =(2,0,2) and j = (0,1,0). Show all work. a=arrow_forwardFor the following function, find the full power series centered at a of convergence. 0 and then give the first 5 nonzero terms of the power series and the open interval = f(2) Σ 8 1(x)--(-1)*(3)* n=0 ₤(x) = + + + ++... The open interval of convergence is: 1 1 3 f(x)= = 28 3x6 +1 (Give your answer in help (intervals) .)arrow_forward
- For the following function, find the full power series centered at x = 0 and then give the first 5 nonzero terms of the power series and the open interval of convergence. f(x) = Σ| n=0 9 f(x) = 6 + 4x f(x)− + + + ++··· The open interval of convergence is: ☐ (Give your answer in help (intervals) .)arrow_forwardLet X be a random variable with the standard normal distribution, i.e.,X has the probability density functionfX(x) = 1/√2π e^-(x^2/2)2 .Consider the random variablesXn = 20(3 + X6) ^1/2n e ^x^2/n+19 , x ∈ R, n ∈ N.Using the dominated convergence theorem, prove that the limit exists and find it limn→∞E(Xn)arrow_forwardLet X be a discrete random variable taking values in {0, 1, 2, . . . }with the probability generating function G(s) = E(sX). Prove thatVar(X) = G′′(1) + G′(1) − [G′(1)]2.[5 Marks](ii) Let X be a random variable taking values in [0,∞) with proba-bility density functionfX(u) = (5/4(1 − u^4, 0 ≤ u ≤ 1,0, otherwise. Let y =x^1/2 find the probability density function of Yarrow_forward
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