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Math
Calculus
Calculus, Early Transcendentals
Chapter 14.6, Problem 46E
Chapter 14.6, Problem 46E
BUY
Calculus, Early Transcendentals
9th Edition
ISBN:
9781337613927
Author: Stewart
Publisher:
CENGAGE L
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1 Functions And Models
2 Limits And Derivatives
3 Differentiation Rules
4 Applications Of Differentiation
5 Integrals
6 Applications Of Integration
7 Techniques Of Integration
8 Further Applications Of Integration
9 Differential Equations
10 Parametric Equations And Polar Coordinates
11 Sequences, Series, And Power Series
12 Vectors And The Geometry Of Space
13 Vector Functions
14 Partial Derivatives
15 Multiple Integrals
16 Vector Calculus
A Numbers, Inequalities, And Absolute Values
B Coordinate Geometry And Lines
C Graphs Of Second-degree Equations
D Trigonometry
E Sigma Notation
F Proofs Of Theorems
G The Logarithm Defined As An Integral
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14.1 Functions Of Several Variables
14.2 Limits And Continuity
14.3 Partial Derivatives
14.4 Tangent Planes And Linear Approximations
14.5 The Chain Rule
14.6 Directional Derivatives And The Gradient Vector
14.7 Maximum And Minimum Values
14.8 Lagrange Multipliers
Chapter Questions
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Problem 1E: Level curves for barometric pressure (in millibars) arc shown for 6:00 am on a day in November. A...
Problem 2E: The contour map shows the average maximum temperature for November 2004 (in C). Estimate the value...
Problem 3E
Problem 4E: Find the directional derivative of f at the given point in the direction indicated by the angle . 4....
Problem 5E: Find the directional derivative of f at the given point in the direction indicated by the angle . 5....
Problem 6E: Find the directional derivative of f at the given point in the direction indicated by the angle . 6....
Problem 7E: Find the directional derivative of f at the given point in the direction indicated by the angle ....
Problem 8E: (a) Find the gradient of f . (b) Evaluate the gradient at the point P . (c) Find the rate of change...
Problem 9E: (a) Find the gradient of f. (b) Evaluate the gradient at the point P. (c) Find the rate of change of...
Problem 10E: (a) Find the gradient of f. (b) Evaluate the gradient at the point P. (c) Find the rate of change of...
Problem 11E: (a) Find the gradient of f. (b) Evaluate the gradient at the point P. (c) Find the rate of change of...
Problem 12E: (a) Find the gradient of f. (b) Evaluate the gradient at the point P. (c) Find the rate of change of...
Problem 13E: Find the directional derivative of the function at the given point in the direction of the vector v....
Problem 14E: Find the directional derivative of the function at the given point in the direction of the vector v....
Problem 15E: Find the directional derivative of the function at the given point in the direction of the vector v....
Problem 16E
Problem 17E: Find the directional derivative of the function at the given point in the direction of the vector v....
Problem 18E: Find the directional derivative of the function at the given point in the direction of the vector v....
Problem 19E: Find the directional derivative of the function at the given point in the direction of the vector v....
Problem 20E: Use the figure to estimate Du, f(2, 2).
Problem 21E
Problem 22E: Find the directional derivative of the function at the point P in the direction of the point Q. 22....
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E: Find the maximum rate of change of f at the given point and the direction in which it occurs. 27....
Problem 28E: Find the maximum rate of change of f at the given point and the direction in which it occurs. 28....
Problem 29E: Find the maximum rate of change of f at the given point and the direction in which it occurs. 23....
Problem 30E: Find the maximum rate of change of f at the given point and the direction in which it occurs. 24....
Problem 31E: Find the maximum rate of change of f at the given point and the direction in which it occurs. 25....
Problem 32E: Find the maximum rate of change of f at the given point and the direction in which it occurs. 26....
Problem 33E
Problem 34E: Find the directions in which the directional derivative of f(x, y) = x2 + xy3 at the point (2, 1)...
Problem 35E: Find all points at which the direction of fastest change of the function f(x, y) = x2 + y2 2x 4y...
Problem 36E: Near a buoy, the depth of a lake at the point with coordinates (x, y) is z = 200 + 0.02x2 0.00 ly3,...
Problem 37E: The temperature T in a metal ball is inversely proportional to the distance from the center of the...
Problem 38E
Problem 39E: Suppose that over a certain region of space the electrical potential V is given by V(x, y, z) = 5x2 ...
Problem 40E: Suppose you are climbing a hill whose shape is given by the equation z = 1000 0.005x2 0.0ly2,...
Problem 41E
Problem 42E: Shown is a topographic map of Blue River Pine Provincial Pork in British Columbia. Draw curves of...
Problem 43E: Show that the operation of taking the gradient of a function has the given property. Assume that u...
Problem 44E: Sketch the gradient vector f(4. 6) for the function f whose level curves are shown. Explain how you...
Problem 45E
Problem 46E
Problem 47E: Find equations of (a) the tangent plane and (b) the normal line to the given surface at the...
Problem 48E: Find equations of (a) the tangent plane and (b) the normal line to the given surface at the...
Problem 49E: Find equations of (a) the tangent plane and (b) the normal line to the given surface at the...
Problem 50E: Find equations of (a) the tangent plane and (b) the normal line to the given surface at the...
Problem 51E: Find equations of (a) the tangent plane and (b) the normal line to the given surface at the...
Problem 52E: Find equations of (a) the tangent plane and (b) the normal line to the given surface at the...
Problem 53E
Problem 54E
Problem 55E: If f(x, y) = xy, find the gradient vector f(3, 2) and use it to find the tangent line to the level...
Problem 56E: If g(x, y) = x2 + y2 4x, find the gradient vector g(1, 2) and use it to find the tangent line to...
Problem 57E: Show that the equation of the tangent plane to the ellipsoid x2/a2 + y2/b2 + z2/c2 = 1 at the point...
Problem 58E: Find the equation of the tangent plane to the hyperboloid x2/a2 + y2/b2 z2/c2 = 1 at (x0. y0. z0)...
Problem 59E
Problem 60E: At what point on the ellipsoid x2 + y2 + 2z2 = 1 is the tangent plane parallel to the plane x + 2y +...
Problem 61E: Are there any points on the hyperboloid x2 y2 z2 = 1 where the tangent plane is parallel to the...
Problem 62E: Show that the ellipsoid 3x2 + 2y2 + z2 = 9 and the sphere x2 + y2 + z2 8x 6y 8z + 24 = 0 arc...
Problem 63E: Show that every plane that is tangent to the cone x2 + y2 = z2 passes through the origin.
Problem 64E: Show that every normal line to the sphere x2 + y2 + z2 = r2 passes through the center of the sphere.
Problem 65E: Where does the normal line to the paraboloid z = x2 + y2 at the point (1, 1, 2) intersect the...
Problem 66E
Problem 67E: Show that the sum of the x-, y-, and z-intercepts of any tangent plane to the surface x+y+z=cis a...
Problem 68E
Problem 69E: Find parametric equations tor the tangent line to the curve of intersection of the paraboloid z = x2...
Problem 70E: (a) The plane y + z = 3 intersects the cylinder x2 +y2 = 5 in an ellipse. Find parametric equations...
Problem 71E: Where does the helix r(t) = cos t, sin t, t intersect the paraboloid z = x2 + y2? What is the angle...
Problem 72E
Problem 73E: Orthogonal Surfaces Two surfaces are called orthogonal at a point of intersection if their normal...
Problem 74E: Orthogonal Surfaces Two surfaces are called orthogonal at a point of intersection if their normal...
Problem 75E: Suppose that the directional derivatives of f(x, y) are known at a given point in two nonparallel...
Problem 76E
Problem 77E
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