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Math 2510 Take Home 3 2. Fubini? Consider the function al Use the substitution u-xy (treating...
(3 points) Consider the indefinite integral X – 3 (3x - 2)2 dx. The substitution u...
(3 points) Consider the indefinite integral X – 3 (3x - 2)2 dx. The substitution u = 3x – 2 transforms the integral into: | du (This answer must be a function of u.) Note: You are not asked to evaluate the integral.
1. Use Green's theorem to evaluate the integral $ xy dx - x^2 y^3 dy, where...
1. Use Green's theorem to evaluate the integral $ xy dx - x^2 y^3 dy, where C is the triangle with vertices (0,0), (1,0) y (1,2)
12. Consider the region bounded above by the function ?=1/(?+2)2(?+6)^2 and below by the xy-plane for...
12. Consider the region bounded above by the function
?=1/(?+2)2(?+6)^2 and below by the xy-plane for x≥0 and ?≥0.
(1 point) Consider the region bounded above by the function z = - "2" (x + 2)2(y + 62 an and below by the xy-plane for x > 0 and y 2 0. On a piece of paper, sketch the shadow of the region in the xy-plane. Set up double integrals to compute the volume of the solid region in two...
24. Consider a consumer with a utility function of u(x,y)=xy. (10 total) a) Draw to scale...
24. Consider a consumer with a utility function of u(x,y)=xy. (10 total) a) Draw to scale the consumer's indifference curves for u(x,y)=100 and u(xy)=400. (2) b) Verify the both x and y are "goods" rather than "bads." (3) c) Verify that the law of diminishing marginal rate of substitution holds. (3) d) Suppose that the utility numbers assigned to bundles are determined by the formula (xy) Vxy, instead of u(x,y)= xy. How does the change in the formula change the...
find the function y=y(x) for x>0 which satisfies the seperable differential equation, dy/dx=(4+17x)/(xy^2), x>0, y(1)=3
find the function y=y(x) for x>0 which satisfies the seperable differential equation, dy/dx=(4+17x)/(xy^2), x>0, y(1)=3
Consider the differential equation: (7y sin(xy) + 2 sec x) dx = (2 lny – 4x...
Consider the differential equation: (7y sin(xy) + 2 sec x) dx = (2 lny – 4x sin(xy))dy Note: Do not use square brackets in your response, use normal parantheses if you have to, i.e "0" Then aM ду and ƏN ax Is this equation exact? Yes No Consider the differential equation: sin(x)dx + 5y cos(x)dy = 0 Which of the following can be an integrating factor to make the equation exact? Select all that apply. On=e-54 On=tan(x) Ju=e-542/2 On =...
Solve the initial value problem 2yy' + 2 = y2 + 2x with y(0) = 4. To solve this, we should use the substitution u = With this substitution, y = y' = Enter derivatives using prime notation (e.g., you would enter y' for dy/dx). After the substitution from t
Solve the initial value problem 2yy' + 2 = y2 + 2x with y(0) = 4. To solve this, we should use the substitution u = With this substitution, y = y' = Enter derivatives using prime notation (e.g., you would enter y' for dy/dx). After the substitution from the previous part, we obtain the following linear differential equation in x, u, u'. The solution to the original initial value problem is described by the following equation in x, y.
Bb Take Test: MATH 216 SUMMER 2 X Bb Blackboard Collaborate Ultra - M X X...
Bb Take Test: MATH 216 SUMMER 2 X Bb Blackboard Collaborate Ultra - M X X c olearn.okan.edu.tr/webapps/assessment/take/launch.jsp?course_assessment_id=_9160_18_course_id=_11453_18_content_id=_118194_1&step=null K ... Remaining Time: 1 hour, 14 minutes, 34 seconds Question Completion Status QUESTION 19 4 points Save Aww. Find the solution to the initial value problem dy 6.xy + y2 + (3x2 + 2xy + 2y) de =0 y(1) = 3 ry+r+y2 + y² + x = 22 3x+y +2.c?y++2r2 + 2y = 24 6.ry + 2y2 + = 37 00....
The Implicit Function Theorem and the Marginal Rate of Substitution (4 Points) 3 An important result...
The Implicit Function Theorem and the Marginal Rate of Substitution (4 Points) 3 An important result from multivariable calculus is the implicit function theorem which states that given a function f (x,y), the derivative of y with respect to a is given by where of/bx denotes the partial derivative of f with respect to a and af/ay denotes the partial derivative of f with respect to y. Simply stated, a partial derivative of a multivariable function is the derivative of...
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
(3 points) Consider the indefinite integral X – 3 (3x - 2)2 dx. The substitution u = 3x – 2 transforms the integral into: | du (This answer must be a function of u.) Note: You are not asked to evaluate the integral.
1. Use Green's theorem to evaluate the integral $ xy dx - x^2 y^3 dy, where C is the triangle with vertices (0,0), (1,0) y (1,2)
12. Consider the region bounded above by the function
?=1/(?+2)2(?+6)^2 and below by the xy-plane for x≥0 and ?≥0.
(1 point) Consider the region bounded above by the function z = - "2" (x + 2)2(y + 62 an and below by the xy-plane for x > 0 and y 2 0. On a piece of paper, sketch the shadow of the region in the xy-plane. Set up double integrals to compute the volume of the solid region in two...
24. Consider a consumer with a utility function of u(x,y)=xy. (10 total) a) Draw to scale the consumer's indifference curves for u(x,y)=100 and u(xy)=400. (2) b) Verify the both x and y are "goods" rather than "bads." (3) c) Verify that the law of diminishing marginal rate of substitution holds. (3) d) Suppose that the utility numbers assigned to bundles are determined by the formula (xy) Vxy, instead of u(x,y)= xy. How does the change in the formula change the...
Consider the differential equation: (7y sin(xy) + 2 sec x) dx = (2 lny – 4x sin(xy))dy Note: Do not use square brackets in your response, use normal parantheses if you have to, i.e "0" Then aM ду and ƏN ax Is this equation exact? Yes No Consider the differential equation: sin(x)dx + 5y cos(x)dy = 0 Which of the following can be an integrating factor to make the equation exact? Select all that apply. On=e-54 On=tan(x) Ju=e-542/2 On =...
Bb Take Test: MATH 216 SUMMER 2 X Bb Blackboard Collaborate Ultra - M X X c olearn.okan.edu.tr/webapps/assessment/take/launch.jsp?course_assessment_id=_9160_18_course_id=_11453_18_content_id=_118194_1&step=null K ... Remaining Time: 1 hour, 14 minutes, 34 seconds Question Completion Status QUESTION 19 4 points Save Aww. Find the solution to the initial value problem dy 6.xy + y2 + (3x2 + 2xy + 2y) de =0 y(1) = 3 ry+r+y2 + y² + x = 22 3x+y +2.c?y++2r2 + 2y = 24 6.ry + 2y2 + = 37 00....
The Implicit Function Theorem and the Marginal Rate of Substitution (4 Points) 3 An important result from multivariable calculus is the implicit function theorem which states that given a function f (x,y), the derivative of y with respect to a is given by where of/bx denotes the partial derivative of f with respect to a and af/ay denotes the partial derivative of f with respect to y. Simply stated, a partial derivative of a multivariable function is the derivative of...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
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