Calculus Volume 316th EditionGilbert Strang, Edwin Jed Herman Publisher: OpenStaxISBN: 9781938168079
Calculus Volume 3
Solutions for Calculus Volume 3
Problem 1E:
For the following exercises, consider points P(1,3) , Q(1,5) , and R(3,7) . Determine the requested...Problem 2E:
For the following exercises, consider points P(1,3) , Q(1,5) , and R(3,7) . Determine the requested...Problem 3E:
For the following exercises, consider points P(1,3) , Q(1,5) , and R(3,7) . Determine the requested...Problem 4E:
For the following exercises, consider points P(1,3) , Q(1,5) , and R(3,7) . Determine the requested...Problem 5E:
For the following exercises, consider points P(1,3) , Q(1,5) , and R(3,7) . Determine the requested...Problem 6E:
For the following exercises, consider points P(1,3) , Q(1,5) , and R(3,7) . Determine the requested...Problem 7E:
For the following exercises, consider points P(1,3) , Q(1,5) , and R(3,7) . Determine the requested...Problem 8E:
For the following exercises, consider points P(1,3) , Q(1,5) , and R(3,7) . Determine the requested...Problem 9E:
For the following exercises, consider points P(1,3) , Q(1,5) , and R(3,7) . Determine the requested...Problem 10E:
For the following exercises, consider points P(1,3) , Q(1,5) , and R(3,7) . Determine the requested...Problem 11E:
For the following exercises, consider points P(1,3) , Q(1,5) , and R(3,7) . Determine the requested...Problem 12E:
For the following exercises, consider points P(1,3) , Q(1,5) , and R(3,7) . Determine the requested...Problem 13E:
For the following exercises, consider points P(1,3) , Q(1,5) , and R(3,7) . Determine the requested...Problem 14E:
For the following exercises, consider points P(1,3) , Q(1,5) , and R(3,7) . Determine the requested...Problem 15E:
Far the following exercises, use the given vectors. a and b. Determine the vector sum a+b and...Problem 16E:
Far the following exercises, use the given vectors. a and b. Determine the vector sum a+b and...Problem 17E:
Far the following exercises, use the given vectors. a and b. Determine the vector sum a+b and...Problem 18E:
Far the following exercises, use the given vectors. a and b. Determine the vector sum a+b and...Problem 19E:
Far the following exercises, use the given vectors. a and b. Determine the vector sum a+b and...Problem 20E:
Far the following exercises, use the given vectors. a and b. Determine the vector sum a+b and...Problem 21E:
Far the following exercises, use the given vectors. a and b. Determine the vector sum a+b and...Problem 22E:
Far the following exercises, use the given vectors. a and b. Determine the vector sum a+b and...Problem 23E:
Far the following exercises, use the given vectors. a and b. Determine the vector sum a+b and...Problem 24E:
Far the following exercises, use the given vectors. a and b. Determine the vector sum a+b and...Problem 25E:
For the following exercises, find vector v with the given magnitude and in the same direction as...Problem 26E:
For the following exercises, find vector v with the given magnitude and in the same direction as...Problem 27E:
For the following exercises, find vector v with the given magnitude and in the same direction as...Problem 28E:
For the following exercises, find vector v with the given magnitude and in the same direction as...Problem 29E:
For the following exercises, find the component form of vector u, given its magnitude and the angle...Problem 30E:
For the following exercises, find the component form of vector u, given its magnitude and the angle...Problem 31E:
For the following exercises, find the component form of vector u, given its magnitude and the angle...Problem 32E:
For the following exercises, find the component form of vector u, given its magnitude and the angle...Problem 33E:
For the following exercises, find the component form of vector u, given its magnitude and the angle...Problem 34E:
For the following exercises, find the component form of vector u, given its magnitude and the angle...Problem 35E:
For the following exercises, vector u is given. Find the angle [0,2) that vector u makes with the...Problem 36E:
For the following exercises, vector u is given. Find the angle [0,2) that vector u makes with the...Problem 37E:
Let a=a1,a2,b=b1,b2 , and c=c1,c2 be three nonzero vectors. If a1b2a2b10 , then show there are two...Problem 39E:
Let P(x0,f(x0)) be a fixed point on the graph of the differential function f with a domain that is...Problem 40E:
Consider the function f(x)=x4 , where x. Determine the real number z0 Such that point Q(2,z0)...Problem 41E:
Consider f and g two functions defined on the same set of real numbers D . Let a=x,f(x) and b=x,g(x)...Problem 43E:
Calculate the coordinates of point D such that ABCD is a parallelogram, with A(1,1),B(2,4), and...Problem 44E:
Consider the points A(2,1),B(10,6),C(13,4) , and D(16,2) . Determine the component form of vector AD...Problem 45E:
The speed of an object is the magnitude of its related velocity vector. A football thrown by a...Problem 46E:
A baseball player throws a baseball at an angle of 30 with the horizontal. If the initial speed of...Problem 47E:
A bullet is fired with an initial velocity of 1500ft/sec at an angle of 60 with the horizontal. Find...Problem 48E:
[T] A 65kg sprinter exerts a force of 798N at a 19 angle with respect to the ground 011 the starting...Problem 49E:
[T] Two forces, a horizontal force of 45lb and another of 52lb , act on the same object. The angle...Problem 50E:
[T] Two fumes, a vertical fence of 26lb and another of 45lb , act on the same object. The angle...Problem 51E:
[T] Three forces act an object. Two of the fences have the magnitudes 58N and 27N , and make angles...Problem 52E:
Three forces with magnitudes 80lb,120lb, and 60lb act on an abject at angles of 45,60 and 30 ,...Problem 53E:
[T] An airplane is flying in the direction of 43 east of north (also abbreviated as N43E ) at a...Problem 54E:
[T] A boat is traveling in the water at 30mph in a direction of N20E (that is, 20 east of north). A...Problem 55E:
[T] A 50-lb weight is hung by a cable so that the two portions of the cable make angles of 40 and 53...Problem 56E:
[T] A 62-lh weight hangs from a nope that makes the angles of 29 and 61 , respectively, with the...Problem 57E:
[T] A 1500lb boat is parked on a ramp that makes an angle of 30 with the horizontal. The boat’s...Problem 58E:
[T] An 85lb box is at rest on a 26 incline. Determine the magnitude of the fame parallel to the...Browse All Chapters of This Textbook
Chapter 1 - Parametric Equations And Polar CoordinatesChapter 1.1 - Parametric EquationsChapter 1.2 - Calculus Of Parametric CurvesChapter 1.3 - Polar CoordinatesChapter 1.4 - Area And Arc Length In Polar CoordinatesChapter 1.5 - Conic SectionsChapter 2 - Vectors In SpaceChapter 2.1 - Vectors In The PlaneChapter 2.2 - Vectors In Three DimensionsChapter 2.3 - The Dot Product
Chapter 2.4 - The Cross ProductChapter 2.5 - Equations Of Lines And Planes In SpaceChapter 2.6 - Quadric SurfacesChapter 2.7 - Cylindrical And Spherical CoordinatesChapter 3 - Vector-valued FunctionsChapter 3.1 - Vector-valued Functions And Space CurvesChapter 3.2 - Calculus Of Vector-valued FunctionsChapter 3.3 - Arc Length And CurvatureChapter 3.4 - Motion In SpaceChapter 4 - Differentiation Of Functions Of Several VariablesChapter 4.1 - Functions Of Several VariablesChapter 4.2 - Limits And ContinuityChapter 4.3 - Partial DerivativesChapter 4.4 - Tangent Planes And Linear ApproximationsChapter 4.5 - The Chain RuleChapter 4.6 - Directional Derivatives And The GradientChapter 4.7 - Maxima/minima ProblemsChapter 4.8 - Lagrange MultipliersChapter 5 - Multiple IntegrationChapter 5.1 - Double Integrals Over Rectangular RegionsChapter 5.2 - Double Integrals Over General RegionsChapter 5.3 - Double Integrals In Polar CoordinatesChapter 5.4 - Triple IntegralsChapter 5.5 - Triple Integrals In Cylindrical And Spherical CoordinatesChapter 5.6 - Calculating Centers Of Mass And Moments Of InertiaChapter 5.7 - Change Of Variables In Multiple IntegralsChapter 6 - Vector CalculusChapter 6.1 - Vector FieldsChapter 6.2 - Line IntegralsChapter 6.3 - Conservative Vector FieldsChapter 6.4 - Green's TheoremChapter 6.5 - Divergence And CurlChapter 6.6 - Surface IntegralsChapter 6.7 - Stokes' TheoremChapter 6.8 - The Divergence TheoremChapter 7 - Second-order Differential EquationsChapter 7.1 - Second-order Linear EquationsChapter 7.2 - Nonhomogeneous Linear EquationsChapter 7.3 - ApplicationsChapter 7.4 - Series Solutions Of Differential Equations
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