Multivariable Calculus
8th Edition
ISBN: 9781305266643
Author: James Stewart
Publisher: Cengage Learning
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Textbook Question
Chapter 12, Problem 4RE
Calculate the given quantity if
a = i + j − 2k
b = 3i − 2j + k
c = j − 5k
(a) 2a + 3b
(b) |b|
(c) a · b
(d) a × b
(c) |b × c|
(f) a · (b × c)
(g) c × c
(h) a × (b × c)
(i) compa b
(j) proja b
(k) The angle between a and b (correct to the nearest degree)
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Chapter 12 Solutions
Multivariable Calculus
Ch. 12.1 - Suppose you start at the origin, move along the...Ch. 12.1 - Sketch the points (1, 5, 3), (0, 2, 3), (3, 0, 2),...Ch. 12.1 - Which of the points A(4, 0, 1), B(3, 1, 5), and...Ch. 12.1 - Prob. 4ECh. 12.1 - What does the equation x = 4 represent in 2? What...Ch. 12.1 - What does the equation y = 3 represent in 3? What...Ch. 12.1 - Describe and sketch the surface in 3 represented...Ch. 12.1 - Describe and sketch the surface in 3 represented...Ch. 12.1 - Find the lengths of the sides of the triangle PQR....Ch. 12.1 - Find the lengths of the sides of the triangle PQR....
Ch. 12.1 - Determine whether the points lie on a straight...Ch. 12.1 - Find the distance from (4, 2, 6) to each of the...Ch. 12.1 - Find an equation of the sphere with center (3, 2,...Ch. 12.1 - Find an equation of the sphere with center (2, 6,...Ch. 12.1 - Find an equation of the sphere that passes through...Ch. 12.1 - Find an equation of the sphere that passes through...Ch. 12.1 - Show that the equation represents a sphere, and...Ch. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - (a) Prove that the midpoint of the line segment...Ch. 12.1 - Find an equation of a sphere if one of its...Ch. 12.1 - Find equations of the spheres with center (2, 3,...Ch. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Prob. 30ECh. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Prob. 32ECh. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Prob. 36ECh. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Prob. 38ECh. 12.1 - Write inequalities to describe the region. 39. The...Ch. 12.1 - Write inequalities to describe the region. 40. The...Ch. 12.1 - Write inequalities to describe the region. 41. The...Ch. 12.1 - Write inequalities to describe the region. 42. The...Ch. 12.1 - Prob. 43ECh. 12.1 - Consider the points P such that the distance from...Ch. 12.1 - Find an equation of the set of all points...Ch. 12.1 - Find the volume of the solid that lies inside both...Ch. 12.1 - Prob. 47ECh. 12.1 - Prob. 48ECh. 12.2 - Are the following quantities vectors or scalars?...Ch. 12.2 - What is the relationship between the point (4, 7)...Ch. 12.2 - Name all the equal vectors in the parallelogram...Ch. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Copy the vectors in the figure and use them to...Ch. 12.2 - In the figure, the tip of c and the tail of d are...Ch. 12.2 - If the vectors in the figure satisfy |u | = | v |...Ch. 12.2 - Find a vector a with representation given by the...Ch. 12.2 - Prob. 10ECh. 12.2 - Find a vector a with representation given by the...Ch. 12.2 - Find a vector a with representation given by the...Ch. 12.2 - Find a vector a with representation given by the...Ch. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Find the sum of the given vectors and illustrate...Ch. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - Find a + b, 4a + 2b, | a |, and | a b | 21. a =...Ch. 12.2 - Prob. 22ECh. 12.2 - Prob. 23ECh. 12.2 - Prob. 24ECh. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - Prob. 27ECh. 12.2 - Prob. 28ECh. 12.2 - Prob. 29ECh. 12.2 - Prob. 30ECh. 12.2 - Prob. 31ECh. 12.2 - Find the magnitude of the resultant force and the...Ch. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - A woman walks due west on the deck of a ship at 3...Ch. 12.2 - Prob. 36ECh. 12.2 - A block-and-tackle pulley hoist is suspended in a...Ch. 12.2 - The tension T at each end of a chain has magnitude...Ch. 12.2 - A boatman wants to cross a canal that is 3 km wide...Ch. 12.2 - Three forces act on an object. Two of the forces...Ch. 12.2 - Find the unit vectors that are parallel to the...Ch. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Let C be the point on the line segment AB that is...Ch. 12.2 - (a) Draw the vectors a = 3, 2, b = 2, 1, and c =...Ch. 12.2 - Suppose that a and b are nonzero vectors that are...Ch. 12.2 - If r = x, y, z and r0 = x0, y0, z0, describe the...Ch. 12.2 - Prob. 48ECh. 12.2 - Prob. 49ECh. 12.2 - Prove Property 5 of vectors algebraically for the...Ch. 12.2 - Use vectors to prove that the line joining the...Ch. 12.2 - Prob. 52ECh. 12.3 - Which of the following expressions are meaningful?...Ch. 12.3 - Prob. 2ECh. 12.3 - Find a b. 3. a = 1.5, 0.4, b = 4, 6Ch. 12.3 - Find a b. 4. a = 6, 2, 3, b = 2, 5, 1Ch. 12.3 - Prob. 5ECh. 12.3 - Find a b. 6. a. = p, p, 2p, b = 2q, q, qCh. 12.3 - Prob. 7ECh. 12.3 - Prob. 8ECh. 12.3 - Find a b. 9. | a | = 7, | b | = 4, the angle...Ch. 12.3 - Find a b. 10. | a | = 80, | b | = 50, the angle...Ch. 12.3 - If u is a unit vector, find u v and u w.Ch. 12.3 - If u is a unit vector, find u v and u w.Ch. 12.3 - (a) Show that i j = j k = k i = 0. (b) Show...Ch. 12.3 - A street vendor sells a hamburgers, b hot dogs,...Ch. 12.3 - Find the angle between the vectors. (First find an...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 - Find, correct to the nearest degree, the three...Ch. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Use vectors to decide whether the triangle with...Ch. 12.3 - Find the values of x such that the angle between...Ch. 12.3 - Prob. 27ECh. 12.3 - Find two unit vectors that make an angle of 60...Ch. 12.3 - Find the acute angle between the lines. 29. 2x y...Ch. 12.3 - Prob. 30ECh. 12.3 - Prob. 31ECh. 12.3 - Find the acute angles between the curves at their...Ch. 12.3 - Prob. 33ECh. 12.3 - Find the direction cosines and direction angles of...Ch. 12.3 - Prob. 35ECh. 12.3 - Prob. 36ECh. 12.3 - Find the direction cosines and direction angles of...Ch. 12.3 - Prob. 38ECh. 12.3 - Prob. 39ECh. 12.3 - Prob. 40ECh. 12.3 - Find the scalar and vector projections of b onto...Ch. 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 - Suppose that a and b are nonzero vectors. (a)...Ch. 12.3 - Prob. 49ECh. 12.3 - A tow truck drags a stalled car along a road. The...Ch. 12.3 - Prob. 51ECh. 12.3 - A boat sails south with the help of a wind blowing...Ch. 12.3 - Use a scalar projection to show that the distance...Ch. 12.3 - If r = x, y, z a = a1, a2, a3, and b = b1, b2, b3,...Ch. 12.3 - Prob. 55ECh. 12.3 - Prob. 56ECh. 12.3 - Prob. 57ECh. 12.3 - If c = | a | b + | b | a, where a, b, and c are...Ch. 12.3 - Prob. 59ECh. 12.3 - Suppose that all sides of a quadrilateral are...Ch. 12.3 - Use Theorem 3 to prove the Cauchy-Schwarz...Ch. 12.3 - The Triangle Inequality for vectors is | a + b | ...Ch. 12.3 - The Parallelogram Law states that | a + b |2 + | a...Ch. 12.3 - Prob. 64ECh. 12.3 - Prob. 65ECh. 12.4 - Find the cross product a b and verify that it is...Ch. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12.4 - Find the cross product a b and verify that it is...Ch. 12.4 - Prob. 7ECh. 12.4 - If a = i 2k and b = j + k, find a b. Sketch a,...Ch. 12.4 - Find the vector, not with determinants, but by...Ch. 12.4 - Find the vector, not with determinants, but by...Ch. 12.4 - Find the vector, not with determinants, but by...Ch. 12.4 - Find the vector, not with determinants, but by...Ch. 12.4 - State whether each expression is meaningful. If...Ch. 12.4 - Find |u v| and determine whether u v is directed...Ch. 12.4 - Find |u v| and determine whether u v is directed...Ch. 12.4 - Prob. 16ECh. 12.4 - If a = 2, 1, 3 and b = 4, 2, 1, find a b and b ...Ch. 12.4 - Prob. 18ECh. 12.4 - Find two unit vectors orthogonal to both 3, 2, 1...Ch. 12.4 - Find two unit vectors orthogonal to both j k and...Ch. 12.4 - Prob. 21ECh. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prove the property of cross products (Theorem 11)....Ch. 12.4 - Prob. 25ECh. 12.4 - Prob. 26ECh. 12.4 - Find the area of the parallelogram with vertices...Ch. 12.4 - Find the area of the parallelogram with vertices...Ch. 12.4 - (a) Find a nonzero vector orthogonal to the plane...Ch. 12.4 - (a) Find a nonzero vector orthogonal to the plane...Ch. 12.4 - (a) Find a nonzero vector orthogonal to the plane...Ch. 12.4 - Prob. 32ECh. 12.4 - Find the volume of the parallelepiped determined...Ch. 12.4 - Find the volume of the parallelepiped determined...Ch. 12.4 - Find the volume of the parallelepiped with...Ch. 12.4 - Prob. 36ECh. 12.4 - Prob. 37ECh. 12.4 - Prob. 38ECh. 12.4 - Prob. 39ECh. 12.4 - Prob. 40ECh. 12.4 - Prob. 41ECh. 12.4 - Let v = 5j and let u be a vector with length 3...Ch. 12.4 - Prob. 43ECh. 12.4 - Prob. 44ECh. 12.4 - (a) Let P be a point not on the line L that passes...Ch. 12.4 - Prob. 47ECh. 12.4 - Prob. 48ECh. 12.4 - Prove that (a b) (a + b) = 2(a b).Ch. 12.4 - Prob. 50ECh. 12.4 - Use Exercise 50 to prove that a (b c) + b (c ...Ch. 12.4 - Prove that (ab)(cd)=|acbcadbd|Ch. 12.4 - Prob. 53ECh. 12.4 - If v1, v2, and v3 are noncoplanar vectors, let...Ch. 12.5 - Determine whether each statement is true or false...Ch. 12.5 - Find a vector equation and parametric equations...Ch. 12.5 - Find a vector equation and parametric equations...Ch. 12.5 - Prob. 4ECh. 12.5 - Find a vector equation and parametric equations...Ch. 12.5 - Prob. 6ECh. 12.5 - Find parametric equations and symmetric equations...Ch. 12.5 - Prob. 8ECh. 12.5 - Find parametric equations and symmetric equations...Ch. 12.5 - Find parametric equations and symmetric equations...Ch. 12.5 - Find parametric equations and symmetric equations...Ch. 12.5 - Find parametric equations and symmetric equations...Ch. 12.5 - Is the line through (4, 6, 1) and (2, 0, 3)...Ch. 12.5 - Prob. 14ECh. 12.5 - (a) Find symmetric equations for the line that...Ch. 12.5 - (a) Find parametric equations for the line through...Ch. 12.5 - Prob. 17ECh. 12.5 - Prob. 18ECh. 12.5 - Determine whether the lines L1 and L2 are...Ch. 12.5 - Prob. 20ECh. 12.5 - Prob. 21ECh. 12.5 - Prob. 22ECh. 12.5 - Find an equation of the plane. 23. The plane...Ch. 12.5 - Prob. 24ECh. 12.5 - Find an equation of the plane. 25. The plane...Ch. 12.5 - Prob. 26ECh. 12.5 - Find an equation of the plane. 27. The plane...Ch. 12.5 - Find an equation of the plane. 28. The plane...Ch. 12.5 - Find an equation of the plane. 29. The plane...Ch. 12.5 - Prob. 30ECh. 12.5 - Find an equation of the plane. 31. The plane...Ch. 12.5 - Find an equation of the plane. 32. The plane...Ch. 12.5 - Find an equation of the plane. 33. The plane...Ch. 12.5 - Prob. 34ECh. 12.5 - Find an equation of the plane. 35. The plane that...Ch. 12.5 - Find an equation of the plane. 36. The plane that...Ch. 12.5 - Find an equation of the plane. 37. The plane that...Ch. 12.5 - Find an equation of the plane. 38. The plane that...Ch. 12.5 - Prob. 39ECh. 12.5 - Prob. 40ECh. 12.5 - Use intercepts to help sketch the plane. 41. 2x +...Ch. 12.5 - Prob. 42ECh. 12.5 - Prob. 43ECh. 12.5 - Prob. 44ECh. 12.5 - Prob. 45ECh. 12.5 - Prob. 46ECh. 12.5 - Find the point at which the line intersects the...Ch. 12.5 - Where does the line through (3, 1, 0) and (1, 5,...Ch. 12.5 - Find direction numbers for the line of...Ch. 12.5 - Prob. 50ECh. 12.5 - Prob. 51ECh. 12.5 - Determine whether the planes are parallel,...Ch. 12.5 - Prob. 53ECh. 12.5 - Determine whether the planes are parallel,...Ch. 12.5 - Prob. 55ECh. 12.5 - Prob. 56ECh. 12.5 - (a) Find parametric equations for the line of...Ch. 12.5 - (a) Find parametric equations for the line of...Ch. 12.5 - Prob. 59ECh. 12.5 - Find symmetric equations for the line of...Ch. 12.5 - Prob. 61ECh. 12.5 - Find an equation for the plane consisting of all...Ch. 12.5 - Prob. 63ECh. 12.5 - (a) Find the point at which the given lines...Ch. 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 - Find the distance between the given parallel...Ch. 12.5 - Find the distance between the given parallel...Ch. 12.5 - Show that the distance between the parallel planes...Ch. 12.5 - Prob. 76ECh. 12.5 - Show that the lines with symmetric equations x = y...Ch. 12.5 - Find the distance between the skew lines with...Ch. 12.5 - Let L1 be the line through the origin and the...Ch. 12.5 - Let L1 be the line through the points (1, 2, 6)...Ch. 12.5 - Prob. 81ECh. 12.5 - Prob. 82ECh. 12.5 - If a, b, and c are not all 0, show that the...Ch. 12.6 - (a) What does the equation y = x2 represent as a...Ch. 12.6 - (a)Sketch the graph of y = ex as a curve in 2. (b)...Ch. 12.6 - Describe and sketch the surface. x2 + z2 = 1Ch. 12.6 - Describe and sketch the surface. 4x2 + y2 = 4Ch. 12.6 - Describe and sketch the surface. z = 1 y2Ch. 12.6 - Describe and sketch the surface. y = z2Ch. 12.6 - Prob. 7ECh. 12.6 - Describe and sketch the surface. z = sin yCh. 12.6 - (a) Find and identify the traces of the quadric...Ch. 12.6 - (a) Find and identify the traces of the quadric...Ch. 12.6 - Prob. 11ECh. 12.6 - Use traces to sketch and identify the surface. 4x2...Ch. 12.6 - Use traces to sketch and identify the surface. x2...Ch. 12.6 - Prob. 14ECh. 12.6 - Use traces to sketch and identify the surface. 9y2...Ch. 12.6 - Prob. 16ECh. 12.6 - Prob. 17ECh. 12.6 - Use traces to sketch and identify the surface. 3x2...Ch. 12.6 - Prob. 19ECh. 12.6 - Use traces to sketch and identify the surface. x =...Ch. 12.6 - Match the equation with its graph (labeled...Ch. 12.6 - Match the equation with its graph (labeled...Ch. 12.6 - Match the equation with its graph (labeled...Ch. 12.6 - Match the equation with its graph (labeled...Ch. 12.6 - Match the equation with its graph (labeled...Ch. 12.6 - Match the equation with its graph (labeled...Ch. 12.6 - Match the equation with its graph (labeled...Ch. 12.6 - Match the equation with its graph (labeled...Ch. 12.6 - Prob. 29ECh. 12.6 - Prob. 30ECh. 12.6 - Prob. 31ECh. 12.6 - Reduce the equation to one of the standard forms,...Ch. 12.6 - Prob. 33ECh. 12.6 - Prob. 34ECh. 12.6 - Prob. 35ECh. 12.6 - Reduce the equation to one of the standard forms,...Ch. 12.6 - Prob. 37ECh. 12.6 - Reduce the equation to one of the standard forms,...Ch. 12.6 - Sketch the region bounded by the surfaces z=x2+y2...Ch. 12.6 - Sketch the region bounded by the paraboloids z =...Ch. 12.6 - Prob. 45ECh. 12.6 - Find an equation for the surface obtained by...Ch. 12.6 - Find an equation for the surface consisting of all...Ch. 12.6 - Find an equation for the surface consisting of all...Ch. 12.6 - Traditionally, the earths surface has been modeled...Ch. 12.6 - A cooling tower for a nuclear reactor is to be...Ch. 12.6 - Show that if the point (a, b, c) lies on the...Ch. 12.6 - Show that the curve of intersection of the...Ch. 12 - What is the difference between a vector and a...Ch. 12 - Prob. 2RCCCh. 12 - If a is a vector and c is a scalar, how is ca...Ch. 12 - Prob. 4RCCCh. 12 - Prob. 5RCCCh. 12 - Prob. 6RCCCh. 12 - Prob. 7RCCCh. 12 - Prob. 8RCCCh. 12 - Prob. 9RCCCh. 12 - Prob. 10RCCCh. 12 - Prob. 11RCCCh. 12 - Prob. 12RCCCh. 12 - Write a vector equation, parametric equations, and...Ch. 12 - Prob. 14RCCCh. 12 - Prob. 15RCCCh. 12 - (a) Describe a method for determining whether...Ch. 12 - Prob. 17RCCCh. 12 - What are the traces of a surface? How do you find...Ch. 12 - Write equations in standard form of the six types...Ch. 12 - Prob. 1RQCh. 12 - Prob. 2RQCh. 12 - Prob. 3RQCh. 12 - Prob. 4RQCh. 12 - Prob. 5RQCh. 12 - Prob. 6RQCh. 12 - Prob. 7RQCh. 12 - Prob. 8RQCh. 12 - Prob. 9RQCh. 12 - Prob. 10RQCh. 12 - Prob. 11RQCh. 12 - Determine whether the statement is true or false....Ch. 12 - Prob. 13RQCh. 12 - Prob. 14RQCh. 12 - Prob. 15RQCh. 12 - Prob. 16RQCh. 12 - Prob. 17RQCh. 12 - Determine whether the statement is true or false....Ch. 12 - Prob. 19RQCh. 12 - Prob. 20RQCh. 12 - Prob. 21RQCh. 12 - Prob. 22RQCh. 12 - Prob. 1RECh. 12 - Prob. 2RECh. 12 - If u and v are the vectors shown in the figure,...Ch. 12 - Calculate the given quantity if a = i + j 2k b =...Ch. 12 - Prob. 5RECh. 12 - Find two unit vectors that are orthogonal to both...Ch. 12 - Suppose that u (v w) = 2. Find (a) (u v) w (b)...Ch. 12 - Show that if a, b, and c are in V3, then (a b) ...Ch. 12 - Find the acute angle between two diagonals of a...Ch. 12 - Prob. 10RECh. 12 - (a) Find a vector perpendicular to the plane...Ch. 12 - Prob. 12RECh. 12 - Prob. 13RECh. 12 - Prob. 14RECh. 12 - Find parametric equations for the line. 15. The...Ch. 12 - Find parametric equations for the line. 16. The...Ch. 12 - Find parametric equations for the line. 17. The...Ch. 12 - Find an equation of the plane. 18. The plane...Ch. 12 - Find an equation of the plane. 19. The plane...Ch. 12 - Find an equation of the plane. 20. The plane...Ch. 12 - Prob. 21RECh. 12 - Find the distance from the origin to the line x =...Ch. 12 - Prob. 23RECh. 12 - Prob. 24RECh. 12 - Prob. 25RECh. 12 - (a) Find an equation of the plane that passes...Ch. 12 - Find the distance between the planes 3x + y 4z =...Ch. 12 - Identify and sketch the graph of each surface. 28....Ch. 12 - Identify and sketch the graph of each surface. 29....Ch. 12 - Identify and sketch the graph of each surface. 30....Ch. 12 - Identify and sketch the graph of each surface. 31....Ch. 12 - Identify and sketch the graph of each surface. 32....Ch. 12 - Identify and sketch the graph of each surface. 33....Ch. 12 - Identify and sketch the graph of each surface. 34....Ch. 12 - Identify and sketch the graph of each surface. 35....Ch. 12 - Prob. 36RECh. 12 - An ellipsoid is created by rotating the ellipse...Ch. 12 - A surface consists of all points P such that the...Ch. 12 - Prob. 1PCh. 12 - Prob. 2PCh. 12 - Suppose v1 and v2 are vectors with |v1| = 2, |v2 |...
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- ... +① العنوان > पर ined sove in peaper ང་ PU+965 Q2// Draw and Evaluate, or Integrate, the function f(u, v) = (1+u2+v²)3 over the region enclosed by one loop of the lemniscate (u² + v²)² - (u² + v²) = 0. Lake 2 4-2² y 7357 r QI// Evaluate f²² cos(y) dxdydz. 4-y 이arrow_forwardし ined sove in peaper Anot in PV+96252 √4-x²-y² Q4// Convert √ √ √2x-x2 √√4-x-2_ 21xy² dzdydx to (a) cylindrical coordinates, (b) Spherical coordinates. ln3 (m3)2-x2 Q Draw and Evaluate Lake √x²+ dydarrow_forward: +0 1 R2X2 العنوان I need a detailed drawing with explanation L L 2) slots per pole per phase = 3/31 B = 180-60 msl Kd Kol, Sin (Info) Isin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 6 50105 1000 S=1000-950 Loco mem 6. Copper losses: 5kw Rotor input loo kw 0.05 اذا ميريد شرح الكتب فقط look 7) rotor DC ined sove in peaper PU + 96er Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum if possible. 5100 2n=2√²+n Lake Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum if possible. T (3n)! 00 //Σn=1 (1+n)!(2+n)!" TH Marrow_forward
- ۳/۱ : +♡ العنوان R2 X2 2) slots per pole per phase = 3/31 B-180-60 msl Kd Kas Sin (1) Isin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس بالفراغ 3) Cos (30) 0.866 レ× 4) Rotating 5) Synchronous speed, 120 x 50 G S=1000-950 50105 1000 looo rem > ined sove in pea Copper losses 5kw Rotor input: 5 0.05 (lookw) bos cid PU+965 Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the series' convergence if possible. 7) rotor !!Σn=1 (1-1)" が Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the series' convergence if possible. 5700 Prove that the p-series Σn=11 (p areal constant) converges if, and diverges otherwise. T Τ Lake Marrow_forwardVo)) %TV .. + 1 R2X2 2) slots per pole per phase = 3/31 B-180-60 msl Kol Sin () Isin () Kd تب بس بالفراغ i Cos (30) 0.866 4) Rotating ۳/۱ 5) Synchronous speed; 12 S=1000-950 50 1000 Copper losses: 5kw Rotor input 5 loo kw 0.05 6) I العنوان Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the series' convergence if possible. اذا ميريد شرح الكتب فقط ok 7) rotor ||| DC 11500 30tan¹() 2n=1' m²+1 1:11 > PV + 16°52 Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the series' convergence if possible. 7357 //Σm=1 (m²-5n+6) Lake Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the series' convergence if possible. - (3)(5+)) T d sove in peaper =T Marrow_forwardL ined sove in peaper Anoting PU+965 4 Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum if possible. +1Σm=1 00 sin Sn Lake 55 Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum if possible. 5700 2n=2√2+n Carrow_forward
- Ministry of Higher Education & Scientific Research Babylon University College of Engineering- musayab Homobile Department Subject :Numerical Analyses Stage: Third Time: 90 min Date: 25-4-2023 2nd month exam/2nd semester (2022-2023) Note: Answer all questions, all questions have same degree. Q1:Given the values X 5 7 11 13 17 F(x) 150 392 1452 2366 5202 Evaluate f(9),using Newton's divided difference formula Q2:A slider in a machine moves along a fixed straight rod.its distance (x cm) along the rod is given below for various values of the time.Find the velocity and acceleration of the slider when t=0.3 seconds. t(seconds) 0 X (cm) 30.13 0.1 31.62 0.2 0.3 0.4 0.5 0.6 32.87 33.64 33.95 33.81 33.24 Q3:From the following table,find the area bounded by the curve and x- axis,between the ordinates x=7.74 to x=7.52 using Simpson's 1/3 rule. X y=f(x) 7.47 7.48 1.93 1.95 7.49 1.98 7.50 7.51 7.52 2.01 2.03 2.06 Q4:Given y+x with initial condition y=1 at x=0;find (y) for x=0.1 by Euler's method.…arrow_forwardV ined sove in peaper Pu+96er Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum if possible. 21/11 55 a Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum if possible. 1Σn=1 (2-") n° 3" 6"arrow_forwardL ined sove in peaper Anoting PU+965 4 Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum if possible. +1Σm=1 00 sin Sn Lake 55 Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum if possible. 5700 2n=2√2+n Carrow_forward
- a い पीर ined sove in peaper Pu+9625 Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum if possible. 3" 6" 1Σn=1 (2-") n Lake = Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum 1/n 2" (n-√n -n 2n-1 0 T=1 . if possible.arrow_forwardAnot ined sove in peaper +9198 PU+965 Q3// Draw and Evaluate fƒ³½³¸ x/3 x -dydx x²+y2 Lake Gart Draw and Find the centroid of the region between the parabola x + y² - 4y=0 and the 2x+y=0 in the xy-plane 3+arrow_forward: +0 العنوان I need a detailed drawing with explanation しじ ined sove in peaper Anoting Q4// Draw and Evaluate √√√xy-²sin(y²)dydx PU+96er Lake Ge Q3// Find the volume of the region between the cylinder 2 = y² and the xy- plane that is bounded by the planes x = 1, x = 2, y = -2, and y = 2. T Marrow_forward
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