EBK WEBASSIGN FOR STEWART'S ESSENTIAL C
2nd Edition
ISBN: 9781337772198
Author: Stewart
Publisher: VST
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Textbook Question
Chapter 11.4, Problem 36E
Show that the function is
44. f(x, y) = xy – 5y2
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Each of the following statements is an attempt to show that a given series is convergent or
divergent using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C
(for "correct") if the argument is valid, or enter | (for "incorrect") if any part of the argument is
flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter I.)
☐ 1. For all n > 1,
seriesΣ In(n)
In(n)
converges.
2, 1,
arctan(n)
the series arctan(n)
n³
☐ 4. For all n > 1,
123
converges.
1
n ln(n)
series In(n) diverges.
2n
.
and the seriesΣconverges, so by the Comparison Test,
2, 3, and the series converges, so by the Comparison Test, the
series-3
1
converges.
☐ 6. For all n > 2, In(n) >, and the series Σ converges, so by the Comparison Test, the
seriesΣ
In(n) converges.
Instructions.
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Both in images okk. Instructions.
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Chapter 11 Solutions
EBK WEBASSIGN FOR STEWART'S ESSENTIAL C
Ch. 11.1 - Let g(x, y) = cos(x + 2y). (a) Evaluate g(2, 1)....Ch. 11.1 - Let F(x,y)=1+4y2. (a) Evaluate F(3,1). (b) Find...Ch. 11.1 - Let f(x,y,z)=x+y+z+ln(4x2y2z2). (a) Evaluate f(1,...Ch. 11.1 - Let g(x,y,z)=x3y2z10xyz. (a) Evaluate g(1, 2, 3)....Ch. 11.1 - Find and sketch the domain of the function....Ch. 11.1 - Find and sketch the domain of the function....Ch. 11.1 - Find and sketch the domain of the function. 15....Ch. 11.1 - Find and sketch the domain of the function....Ch. 11.1 - Find and sketch the domain of the function. 19....Ch. 11.1 - Find and sketch the domain of the function. f(x,...
Ch. 11.1 - Find and sketch the domain of the function....Ch. 11.1 - Find and sketch the domain of the function. 22....Ch. 11.1 - Prob. 14ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 15ECh. 11.1 - Sketch the graph of the function. f(x, y) = eyCh. 11.1 - 1320 Sketch the graph of the function. 17. f(x, y)...Ch. 11.1 - Prob. 18ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 19ECh. 11.1 - A contour map for a function f is shown. Use it to...Ch. 11.1 - Two contour maps are shown. One is for a function...Ch. 11.1 - Locate the points A and B on the map of Lonesome...Ch. 11.1 - Make a rough sketch of a contour map for the...Ch. 11.1 - Prob. 25ECh. 11.1 - Draw a contour map of the function showing several...Ch. 11.1 - Draw a contour map of the function showing several...Ch. 11.1 - Prob. 28ECh. 11.1 - Draw a contour map of the function showing several...Ch. 11.1 - Prob. 30ECh. 11.1 - Draw a contour map of the function showing several...Ch. 11.1 - Draw a contour map of the function showing several...Ch. 11.1 - Sketch both a contour map and a graph of the...Ch. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Prob. 37ECh. 11.1 - Use a computer to graph the function using various...Ch. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Prob. 43ECh. 11.1 - Prob. 44ECh. 11.1 - Prob. 45ECh. 11.1 - Prob. 46ECh. 11.1 - Prob. 47ECh. 11.1 - Prob. 48ECh. 11.1 - Prob. 49ECh. 11.1 - Prob. 50ECh. 11.1 - Prob. 51ECh. 11.1 - Prob. 52ECh. 11.1 - Prob. 53ECh. 11.1 - Prob. 55ECh. 11.1 - Prob. 54ECh. 11.1 - Prob. 56ECh. 11.2 - Prob. 1ECh. 11.2 - Prob. 2ECh. 11.2 - Prob. 3ECh. 11.2 - Prob. 4ECh. 11.2 - Prob. 5ECh. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - Prob. 8ECh. 11.2 - Prob. 9ECh. 11.2 - Prob. 10ECh. 11.2 - Prob. 11ECh. 11.2 - Prob. 12ECh. 11.2 - Prob. 13ECh. 11.2 - Prob. 14ECh. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Determine the set of points at which the function...Ch. 11.2 - Determine the set of points at which the function...Ch. 11.2 - Determine the set of points at which the function...Ch. 11.2 - Determine the set of points at which the function...Ch. 11.2 - Determine the set of points at which the function...Ch. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - Prob. 29ECh. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.2 - Prob. 34ECh. 11.3 - Prob. 1ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Prob. 10ECh. 11.3 - Prob. 11ECh. 11.3 - Prob. 12ECh. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Prob. 16ECh. 11.3 - Prob. 17ECh. 11.3 - Prob. 18ECh. 11.3 - Prob. 19ECh. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Find the first partial derivatives of the...Ch. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Find the indicated partial derivative. 32. f(x, y)...Ch. 11.3 - Prob. 33ECh. 11.3 - Prob. 34ECh. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - 3738 Find fx and fy and graph f, fx, and fy with...Ch. 11.3 - Prob. 38ECh. 11.3 - Prob. 39ECh. 11.3 - Use implicit differentiation to find z/x and z/y....Ch. 11.3 - Use implicit differentiation to find z/x and z/y....Ch. 11.3 - Prob. 42ECh. 11.3 - Prob. 43ECh. 11.3 - Find z/x and z/y. 52. (a) z = f(x)g(y) (b) z =...Ch. 11.3 - Prob. 45ECh. 11.3 - Find all the second partial derivatives. 54. f(x,...Ch. 11.3 - Find all the second partial derivatives. 55....Ch. 11.3 - Prob. 48ECh. 11.3 - Prob. 49ECh. 11.3 - Prob. 50ECh. 11.3 - Prob. 51ECh. 11.3 - Verify that the conclusion of Clairauts Theorem...Ch. 11.3 - Prob. 53ECh. 11.3 - Prob. 54ECh. 11.3 - Prob. 55ECh. 11.3 - Prob. 56ECh. 11.3 - Prob. 57ECh. 11.3 - Find the indicated partial derivative(s). 70. u =...Ch. 11.3 - Prob. 59ECh. 11.3 - Prob. 60ECh. 11.3 - Prob. 61ECh. 11.3 - Determine whether each of the following functions...Ch. 11.3 - Verify that the function u=1/x2+y2+z2 is a...Ch. 11.3 - Prob. 64ECh. 11.3 - Prob. 65ECh. 11.3 - Prob. 66ECh. 11.3 - Show that the function z = xey + yex is a solution...Ch. 11.3 - Prob. 68ECh. 11.3 - Prob. 69ECh. 11.3 - Prob. 71ECh. 11.3 - Prob. 70ECh. 11.3 - The wind-chill index is modeled by the function W...Ch. 11.3 - Prob. 73ECh. 11.3 - Prob. 74ECh. 11.3 - Prob. 75ECh. 11.3 - Prob. 76ECh. 11.3 - Prob. 77ECh. 11.3 - Prob. 78ECh. 11.3 - Prob. 79ECh. 11.3 - Prob. 80ECh. 11.3 - Prob. 81ECh. 11.3 - Prob. 82ECh. 11.4 - Find an equation of the tangent plane to the given...Ch. 11.4 - Find an equation of the tangent plane to the given...Ch. 11.4 - Prob. 3ECh. 11.4 - Find an equation of the tangent plane to the given...Ch. 11.4 - Find an equation of the tangent plane to the given...Ch. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 11ECh. 11.4 - Explain why the function is differentiable at the...Ch. 11.4 - Prob. 14ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 15ECh. 11.4 - Verify the linear approximation at (0, 0). 16....Ch. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Prob. 19ECh. 11.4 - Find the differential of the function. 26....Ch. 11.4 - Prob. 21ECh. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - If z = x2 xy + 3y2 and (x, y) changes from (3, 1)...Ch. 11.4 - The length and width of a rectangle are measured...Ch. 11.4 - Use differentials to estimate the amount of metal...Ch. 11.4 - Prob. 29ECh. 11.4 - Prob. 32ECh. 11.4 - Prob. 30ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 31ECh. 11.4 - Suppose you need to know an equation of the...Ch. 11.4 - Show that the function is differentiable by...Ch. 11.4 - Show that the function is differentiable by...Ch. 11.4 - Prob. 37ECh. 11.4 - (a) The function...Ch. 11.5 - Use the Chain Rule to find dz/dt or dw/dt. 1....Ch. 11.5 - Use the Chain Rule to find dz/dt or dw/dt. 2....Ch. 11.5 - Use the Chain Rule to find dz/dt or dw/dt. 5. w =...Ch. 11.5 - Use the Chain Rule to find dz/dt or dw/dt. 6. w =...Ch. 11.5 - Use the Chain Rule to find z/s and z/t. 5....Ch. 11.5 - Use the Chain Rule to find z/s and z/t. 6....Ch. 11.5 - Use the Chain Rule to find z/s and z/t. 11. z = er...Ch. 11.5 - Prob. 8ECh. 11.5 - If z = f(x, y), where f is differentiable, and...Ch. 11.5 - Let W(s,t)=F(u(s,t),(s,t)), where F, u and are...Ch. 11.5 - Suppose f is a differentiable function of x and y,...Ch. 11.5 - Suppose f is a differentiable function of x and y,...Ch. 11.5 - Prob. 13ECh. 11.5 - Prob. 14ECh. 11.5 - Prob. 15ECh. 11.5 - Prob. 16ECh. 11.5 - Use the Chain Rule to find the indicated partial...Ch. 11.5 - Use the Chain Rule to find the indicated partial...Ch. 11.5 - Use the Chain Rule to find the indicated partial...Ch. 11.5 - Use the Chain Rule to find the indicated partial...Ch. 11.5 - Use the Chain Rule to find the indicated partial...Ch. 11.5 - Use Equation 6 to find dy/dx. 28. cos(xy) = 1 +...Ch. 11.5 - Use Equation 6 to find dy/dx. 29. tan1(x2y) = x +...Ch. 11.5 - Use Equation 6 to find dy/dx. 30. ey sin x = x +...Ch. 11.5 - Use Equations 7 to find z/x and z/y. 31. x2 + 2y2...Ch. 11.5 - Use Equations 7 to find z/y and z/y. 26....Ch. 11.5 - Use Equations 7 to find z/x and z/y. 33. ez = xyzCh. 11.5 - Use Equations 7 to find z/x and z/y. 34. yz + x ln...Ch. 11.5 - The temperature at a point (x, y) is T(x, y),...Ch. 11.5 - Prob. 30ECh. 11.5 - The speed of sound traveling through ocean water...Ch. 11.5 - Prob. 32ECh. 11.5 - Prob. 33ECh. 11.5 - The voltage V in a simple electrical circuit is...Ch. 11.5 - The pressure of 1 mole of an ideal gas is...Ch. 11.5 - A sound with frequency fs, is produced by a source...Ch. 11.5 - Assume that all the given functions are...Ch. 11.5 - Assume that all the given functions are...Ch. 11.5 - Assume that all the given functions are...Ch. 11.5 - Prob. 40ECh. 11.5 - Prob. 41ECh. 11.5 - Prob. 42ECh. 11.5 - Prob. 43ECh. 11.5 - Prob. 44ECh. 11.5 - Prob. 45ECh. 11.5 - Prob. 46ECh. 11.5 - Prob. 47ECh. 11.5 - Prob. 48ECh. 11.6 - Find the directional derivative of f at the given...Ch. 11.6 - Find the directional derivative of f at the given...Ch. 11.6 - (a) Find the gradient of f. (b) Evaluate the...Ch. 11.6 - Prob. 4ECh. 11.6 - Prob. 5ECh. 11.6 - (a) Find the gradient of f. (b) Evaluate the...Ch. 11.6 - Prob. 7ECh. 11.6 - Prob. 8ECh. 11.6 - Prob. 9ECh. 11.6 - Prob. 10ECh. 11.6 - Find the directional derivative of the function at...Ch. 11.6 - Use the figure to estimate Du, f(2, 2).Ch. 11.6 - Prob. 13ECh. 11.6 - Prob. 14ECh. 11.6 - Prob. 16ECh. 11.6 - Prob. 15ECh. 11.6 - Find the maximum rate of change of f at the given...Ch. 11.6 - Find the maximum rate of change of f at the given...Ch. 11.6 - (a) Show that a differentiable function f...Ch. 11.6 - Find the directions in which the directional...Ch. 11.6 - Find all points at which the direction of fastest...Ch. 11.6 - Near a buoy, the depth of a lake at the point with...Ch. 11.6 - The temperature T in a metal ball is inversely...Ch. 11.6 - Prob. 24ECh. 11.6 - Suppose that over a certain region of space the...Ch. 11.6 - Suppose you are climbing a hill whose shape is...Ch. 11.6 - Prob. 27ECh. 11.6 - Shown is a topographic map of Blue River Pine...Ch. 11.6 - Show that the operation of taking the gradient of...Ch. 11.6 - Prob. 30ECh. 11.6 - Prob. 31ECh. 11.6 - Prob. 32ECh. 11.6 - Find equations of (a) the tangent plane and (b)...Ch. 11.6 - Find equations of (a) the tangent plane and (b)...Ch. 11.6 - Find equations of (a) the tangent plane and (b)...Ch. 11.6 - Find equations of (a) the tangent plane and (b)...Ch. 11.6 - Use a computer to graph the surface, the tangent...Ch. 11.6 - Use a computer to graph the surface, the tangent...Ch. 11.6 - If f(x, y) = xy, find the gradient vector f(3, 2)...Ch. 11.6 - If g(x, y) = x2 + y2 4x, find the gradient vector...Ch. 11.6 - Show that the equation of the tangent plane to the...Ch. 11.6 - At what point on the paraboloid y=x2+z2 is the...Ch. 11.6 - Are there any points on the hyperboloid x2 y2 z2...Ch. 11.6 - Show that the ellipsoid 3x2 + 2y2 + z2 = 9 and the...Ch. 11.6 - Where does the normal line to the paraboloid z =...Ch. 11.6 - Prob. 46ECh. 11.6 - Show that the sum of the x-, y-, and z-intercepts...Ch. 11.6 - Prob. 48ECh. 11.6 - Find parametric equations tor the tangent line to...Ch. 11.6 - Prob. 50ECh. 11.6 - Prob. 51ECh. 11.6 - Prob. 52ECh. 11.6 - Suppose that the directional derivatives of f(x,...Ch. 11.6 - Prob. 54ECh. 11.7 - Suppose (1, 1) is a critical point of a function f...Ch. 11.7 - Use the level curves in the figure to predict the...Ch. 11.7 - Find the local maximum and minimum values and...Ch. 11.7 - Find the local maximum and minimum values and...Ch. 11.7 - Find the local maximum and minimum values and...Ch. 11.7 - Find the local maximum and minimum values and...Ch. 11.7 - Find the local maximum and minimum values and...Ch. 11.7 - Find the local maximum and minimum values and...Ch. 11.7 - Prob. 9ECh. 11.7 - Prob. 10ECh. 11.7 - Prob. 11ECh. 11.7 - Prob. 12ECh. 11.7 - Prob. 13ECh. 11.7 - Prob. 14ECh. 11.7 - Prob. 15ECh. 11.7 - Prob. 16ECh. 11.7 - Prob. 17ECh. 11.7 - Use a graph or level curves or both to estimate...Ch. 11.7 - Prob. 19ECh. 11.7 - Prob. 20ECh. 11.7 - Use a graphing device as in Example 4 (or Newtons...Ch. 11.7 - Use a graphing device as in Example 4 (or Newtons...Ch. 11.7 - Find the absolute maximum and minimum values of f...Ch. 11.7 - Find the absolute maximum and minimum values of f...Ch. 11.7 - Find the absolute maximum and minimum values of f...Ch. 11.7 - Find the absolute maximum and minimum values of f...Ch. 11.7 - Find the absolute maximum and minimum values of f...Ch. 11.7 - Find the absolute maximum and minimum values of f...Ch. 11.7 - Prob. 29ECh. 11.7 - Prob. 30ECh. 11.7 - Prob. 31ECh. 11.7 - Prob. 32ECh. 11.7 - Prob. 33ECh. 11.7 - Prob. 34ECh. 11.7 - Prob. 35ECh. 11.7 - Prob. 36ECh. 11.7 - Prob. 37ECh. 11.7 - Prob. 38ECh. 11.7 - Prob. 39ECh. 11.7 - Prob. 40ECh. 11.7 - Prob. 41ECh. 11.7 - The base of an aquarium with given volume V is...Ch. 11.7 - Prob. 43ECh. 11.7 - Prob. 44ECh. 11.7 - Prob. 45ECh. 11.7 - Prob. 46ECh. 11.7 - Prob. 47ECh. 11.7 - Prob. 48ECh. 11.8 - Pictured are a contour map of f and a curve with...Ch. 11.8 - Prob. 21ECh. 11.8 - Use Lagrange multipliers to find the maximum and...Ch. 11.8 - Each of these extreme value problems has a...Ch. 11.8 - Use Lagrange multipliers to find the maximum and...Ch. 11.8 - Prob. 4ECh. 11.8 - Each of these extreme value problems has a...Ch. 11.8 - Prob. 6ECh. 11.8 - Use Lagrange multipliers to find the maximum and...Ch. 11.8 - Prob. 8ECh. 11.8 - Prob. 9ECh. 11.8 - Prob. 10ECh. 11.8 - Prob. 11ECh. 11.8 - Prob. 12ECh. 11.8 - Find the extreme values of f subject to both...Ch. 11.8 - Prob. 14ECh. 11.8 - Prob. 15ECh. 11.8 - Prob. 16ECh. 11.8 - Find the extreme values of f on the region...Ch. 11.8 - Prob. 18ECh. 11.8 - Prob. 19ECh. 11.8 - Prob. 22ECh. 11.8 - Prob. 23ECh. 11.8 - Prob. 25ECh. 11.8 - Prob. 26ECh. 11.8 - Use Lagrange multipliers to prove that the...Ch. 11.8 - Use Lagrange multipliers to prove that the...Ch. 11.8 - Use Lagrange multipliers to give an alternate...Ch. 11.8 - Use Lagrange multipliers to give an alternate...Ch. 11.8 - Use Lagrange multipliers to give an alternate...Ch. 11.8 - Use Lagrange multipliers to give an alternate...Ch. 11.8 - Use Lagrange multipliers to give an alternate...Ch. 11.8 - Use Lagrange multipliers to give an alternate...Ch. 11.8 - Use Lagrange multipliers to give an alternate...Ch. 11.8 - Use Lagrange multipliers to give an alternate...Ch. 11.8 - Prob. 37ECh. 11.8 - Prob. 38ECh. 11.8 - Prob. 39ECh. 11.8 - Prob. 40ECh. 11.8 - Prob. 41ECh. 11.8 - Prob. 42ECh. 11.8 - The plane x + y + 2z = 2 intersects the paraboloid...Ch. 11.8 - Prob. 44ECh. 11.8 - (a) Find the maximum value of...Ch. 11.8 - Prob. 48ECh. 11 - Prob. 1RCCCh. 11 - What is a function of three variables? How can you...Ch. 11 - Prob. 3RCCCh. 11 - (a) What does it mean to say that f is continuous...Ch. 11 - Prob. 5RCCCh. 11 - What does Clairauts Theorem say?Ch. 11 - Prob. 7RCCCh. 11 - Define the linearization of f at (a, b). What is...Ch. 11 - Prob. 9RCCCh. 11 - If z = f(x, y), what arc the differentials dx, dy,...Ch. 11 - State the Chain Rule for the case where z = f(x,...Ch. 11 - If z is defined implicitly as a function of x and...Ch. 11 - Prob. 13RCCCh. 11 - Prob. 14RCCCh. 11 - Prob. 15RCCCh. 11 - Prob. 16RCCCh. 11 - State the Second Derivatives Test.Ch. 11 - (a) What is a closed set in 2? What is a bounded...Ch. 11 - Explain how the method of Lagrange multipliers...Ch. 11 - Determine whether the statement is true or false....Ch. 11 - Prob. 2RQCh. 11 - Determine whether the statement is true or false....Ch. 11 - Determine whether the statement is true or false....Ch. 11 - Determine whether the statement is true or false....Ch. 11 - Determine whether the statement is true or false....Ch. 11 - Determine whether the statement is true or false....Ch. 11 - Prob. 8RQCh. 11 - Determine whether the statement is true or false....Ch. 11 - Determine whether the statement is true or false....Ch. 11 - Determine whether the statement is true or false....Ch. 11 - Determine whether the statement is true or false....Ch. 11 - Find and sketch the domain of the function. 1....Ch. 11 - Find and sketch the domain of the function. 2....Ch. 11 - Sketch the graph of the function. 3. f(x, y) = 1 ...Ch. 11 - Sketch the graph of the function. 4. f(x, y) = x2...Ch. 11 - Sketch several level curves of the function. 5....Ch. 11 - Sketch several level curves of the function. 6....Ch. 11 - Make a rough sketch of a contour map for the...Ch. 11 - The contour map of a function f is shown, (a)...Ch. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Prob. 15RECh. 11 - The speed of sound traveling through ocean water...Ch. 11 - Prob. 17RECh. 11 - Prob. 18RECh. 11 - Prob. 19RECh. 11 - Prob. 20RECh. 11 - If z = xy + xey/x show that xzx+yzy=xy+z.Ch. 11 - Prob. 22RECh. 11 - Prob. 23RECh. 11 - Prob. 24RECh. 11 - Prob. 25RECh. 11 - Prob. 26RECh. 11 - Prob. 27RECh. 11 - Prob. 28RECh. 11 - Prob. 29RECh. 11 - Find du if u = ln(1 + se2t).Ch. 11 - Prob. 31RECh. 11 - Prob. 32RECh. 11 - Prob. 33RECh. 11 - If v = x2sin y + yexy, where x = s + 2t and y =...Ch. 11 - Prob. 35RECh. 11 - Prob. 36RECh. 11 - Prob. 37RECh. 11 - The length x of a side of a triangle is increasing...Ch. 11 - Prob. 39RECh. 11 - If cos(xyz) = 1 + .x2y2 + z2, find zx and zy.Ch. 11 - Prob. 41RECh. 11 - Prob. 42RECh. 11 - Prob. 43RECh. 11 - Find the directional derivative of f at the given...Ch. 11 - Find the maximum rate of change of f(x,y)=x2y+y at...Ch. 11 - Find parametric equations of the tangent line at...Ch. 11 - Find the local maximum and minimum values and...Ch. 11 - Find the local maximum and minimum values and...Ch. 11 - Find the local maximum and minimum values and...Ch. 11 - Find the local maximum and minimum values and...Ch. 11 - Find the absolute maximum and minimum values of f...Ch. 11 - Find the absolute maximum and minimum values of f...Ch. 11 - Use a graph or level curves or both to estimate...Ch. 11 - Use a graphing calculator or computer (or Newtons...Ch. 11 - Use Lagrange multipliers to find the maximum and...Ch. 11 - Use Lagrange multipliers to find the maximum and...Ch. 11 - Use Lagrange multipliers to find the maximum and...Ch. 11 - Use Lagrange multipliers to find the maximum and...Ch. 11 - Prob. 59RECh. 11 - A package in the shape of a rectangular box can be...Ch. 11 - A pentagon is formed by placing an isosceles...Ch. 11 - Prob. 62RE
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- Question 1: If a barometer were built using oil (p = 0.92 g/cm³) instead of mercury (p = 13.6 g/cm³), would the column of oil be higher than, lower than, or the same as the column of mercury at 1.00 atm? If the level is different, by what factor? Explain. (5 pts) Solution: A barometer works based on the principle that the pressure exerted by the liquid column balances atmospheric pressure. The pressure is given by: P = pgh Since the atmospheric pressure remains constant (P = 1.00 atm), the height of the liquid column is inversely proportional to its density: Step 1: Given Data PHg hol=hgx Poil • Density of mercury: PHg = 13.6 g/cm³ Density of oil: Poil = 0.92 g/cm³ • Standard height of mercury at 1.00 atm: hμg Step 2: Compute Height of Oil = 760 mm = 0.760 m 13.6 hoil = 0.760 x 0.92 hoil = 0.760 × 14.78 hoil = 11.23 m Step 3: Compare Heights Since oil is less dense than mercury, the column of oil must be much taller than that of mercury. The factor by which it is taller is: Final…arrow_forwardQuestion 3: A sealed flask at room temperature contains a mixture of neon (Ne) and nitrogen (N2) gases. Ne has a mass of 3.25 g and exerts a pressure of 48.2 torr. . N2 contributes a pressure of 142 torr. • What is the mass of the N2 in the flask? • Atomic mass of Ne = 20.1797 g/mol • Atomic mass of N = 14.0067 g/mol Solution: We will use the Ideal Gas Law to determine the number of moles of each gas and calculate the mass of N2. PV = nRT where: • P = total pressure • V volume of the flask (same for both gases) n = number of moles of gas • R 0.0821 L atm/mol K • T = Room temperature (assume 298 K) Since both gases are in the same flask, their partial pressures correspond to their mole fractions. Step 1: Convert Pressures to Atmospheres 48.2 PNe = 0.0634 atm 760 142 PN2 = = 0.1868 atm 760 Step 2: Determine Moles of Ne nNe = mass molar mass 3.25 nNe 20.1797 nne 0.1611 mol Step 3: Use Partial Pressure Ratio to Find narrow_forward"I have written solutions in text form, but I need experts to rewrite them in handwriting from A to Z, exactly as I have written, without any changes."arrow_forward
- 3.12 (B). A horizontal beam AB is 4 m long and of constant flexural rigidity. It is rigidly built-in at the left-hand end A and simply supported on a non-yielding support at the right-hand end B. The beam carries Uniformly distributed vertical loading of 18 kN/m over its whole length, together with a vertical downward load of 10KN at 2.5 m from the end A. Sketch the S.F. and B.M. diagrams for the beam, indicating all main values. Cl. Struct. E.] CS.F. 45,10,376 KN, B.M. 186, +36.15 kNm.7arrow_forwardQize f(x) = x + 2x2 - 2 x² + 4x²² - Solve the equation using Newton Raphsonarrow_forward-b±√√b2-4ac 2a @4x²-12x+9=0 27 de febrero de 2025 -b±√√b2-4ac 2a ⑥2x²-4x-1=0 a = 4 b=-12 c=9 a = 2 b = 9 c = \ x=-42±√(2-4 (4) (9) 2(4)) X = (12) ±√44)-(360) 2(108) x = ±√ X = =±√√²-4(2) (1) 2() X = ±√ + X = X = + X₁ = = X₁ = X₁ = + X₁ = = =arrow_forward
- 3.9 (A/B). A beam ABCDE, with A on the left, is 7 m long and is simply supported at Band E. The lengths of the various portions are AB 1-5m, BC = 1-5m, CD = 1 m and DE : 3 m. There is a uniformly distributed load of 15kN/m between B and a point 2m to the right of B and concentrated loads of 20 KN act at 4 and 0 with one of 50 KN at C. (a) Draw the S.F. diagrams and hence determine the position from A at which the S.F. is zero. (b) Determine the value of the B.M. at this point. (c) Sketch the B.M. diagram approximately to scale, quoting the principal values. [3.32 m, 69.8 KNm, 0, 30, 69.1, 68.1, 0 kNm.]arrow_forward4. Verify that V X (aẢ) = (Va) XẢ + aV X Ả where Ả = xyz(x + y + 2) A and a = 3xy + 4zx by carrying out the detailed differentiations.arrow_forward3. For each of the arrow or quiver graphs shown below, determine analytically V°C and V X Č. From these analytical solutions, identify the extrema (+/-) and plot these points on the arrow graph. (a) C = −✰CosxSiny + ŷSinxCosy -π<ׂу<π Ty (b) C = −xSin2y + ŷCos2y x, y<π -π< (c) C = −xCosx + ŷSiny -π< x, y < πarrow_forward
- 7.10 (B/C). A circular flat plate of diameter 305 mm and thickness 6.35 mm is clamped at the edges and subjected to a Uniform lateral pressure of 345 kN/m². Evaluate: (a) the central deflection, (b) the position and magnitude of the maximum radial stress. C6.1 x 10 m; 149.2 MN/m².] 100 200arrow_forward3.15 (B). A beam ABCD is simply supported at B and C with ABCD=2m; BC 4 m. It carries a point load of 60 KN at the free end A, a Uniformly distributed load of 60 KN/m between B and C and an anticlockwise moment of 80 KN m in the plane of the beam applied at the free end D. Sketch and dimension the S.F. and B.M. diagrams, and determine the position and magnitude of the maximum bending moment. CEL.E.] CS.F. 60, 170, 70KN, B.M. 120, +120.1, +80 kNm, 120.1 kNm at 2.83 m to right of 8.7arrow_forward7.1 (A/B). A Uniform I-section beam has flanges 150 mm wide by 8 mm thick and a web 180 mm wide and 8 mm thick. At a certain section there is a shearing force of 120 KN. Draw a diagram to illustrate the distribution of shear stress across the section as a result of bending. What is the maximum shear stress? [86.7 MN/m².arrow_forward
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