Find the maximum and minimum values of the function f(x, y)-xy subject to g(x, y) = x² + xy + y² = 108

Q: X+5x+1 After decomposing the rational function x³-6x²+9x into partial fractions without evaluating…

A: Given problem:-

Q: Test: Test 2 (11 problems) In the following problem, begin by drawing a diagram that shows the…

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Q: Q2: Find the determinant of 3x3 Matrix. 5 7-8 4-36 1 7-9

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Q: II. Solve the following problems. Enclose final answer. 8.A kite at an altitude of 200 ft. moves…

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Q: Calculate the integral approximation S10 for Si, dx. 1 x5+1 S10 =

A: Let's find integration value by using simpson rule.

Q: 3- dy + 3x^²y = x³6 s dx Y- XLnx dy dy +y = ₂l₁x dx 2Lnx ets

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Q: Q2] Classify the following D.E to: order, degree, homogeneous, and linear: dy 2y=x 3 dx dx

A: We can solve this as follows:

Q: nd the area (in square units) of the region under the graph of the function f on the interval [5,…

A: Given query is to find the area under the curve

Q: 32 Evaluate the integral ·ƒƒ(6-y²) dy dx. 00 The value is 18. (Type a simplified fraction.)

A: We know, ∫xndx=xn+1n+1, for any real number n.

Q: Compute the area of the region enclosed by the curves. X y - 2x², y = x² - 4x -2/25 2

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Q: Examples: 1. Use the graph of f(x) to state the following: a) absolute maximum and absolute minimum…

A: Note that, according to Bartleby guidelines, we can answer only the first question in the case of…

Q: Evaluate the iterated double integral 2 b.) √ √ ² sinπTy ³ dydx

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Q: 2. Determine the angle, to the nearest degree, between the vectors * = (4,6,-2) and y = (1,8,2)

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Q: Find the determinant of the matrix, show all of your work -1 3 5 0 0 1 -2 000000 4 0

A: We need to find the determinant of the following matrix. So,…

Q: e the following function and its graph to answer (a) through (d) below. 6-X, f(x)= 3x x4. Find lim…

A: The given function,fx=6-x,x<43x4+3,x>4

Q: Find the length of the arc of a circle of diameter 8 meters sub tended by a central angle 2pi/3…

A: Let "θ" be a central angle in a circle of radius "r". Let "s" be the length of the arc cut off by…

Q: Evaluate LL²³ S²x² y² وژ sin z6 dx dy dz

A: To evaluate: ∫01 ∫0z2 ∫03 y2sin⁡z6dxdydz Let, I =∫01 ∫0z2 ∫03 y2sin⁡z6dxdydz First integrate with…

Q: Find the volume generated by revolving about y = 2, the area bounded by y² = x-1 and y = -x +3.…

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Q: A ship leaves port at noon and travels at a bearing of 214°. The ship's average rate of speed is 15…

A: NOTE: Refresh your page if you can't see any equations. . the given angle is  the given speed is…

Q: 7 13 8 a Find the area of the shaded region above.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 8 1 X = Σ" with convergence in (-1, 1), find the power series for 1-x n=0 1 - 8x³ 8 n=0 Identify its…

A: Let's find power series and it's interval of converges.

Q: 11. S x + 4 x² + 5x - 6 dx

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Q: Prove that the vectors v= and w= are orthogonal.

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Q: the sum if convergent. 4) 2-6+18-54...

A: In this question, we will evaluate this series and test for convergence.

Q: Using Root Test the series Σtan where n 7n4 an = 3n4 + 4n - 5 diverges since 7 lim an == n→+∞ 3 the…

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Q: Find area inside 3 - 3 cos 0 and outside r = 3 Ⓡ

A: Consider the figure below :

Q: 1) Solve the initial value problem. Show All Your Work. dy 2x+sec² X 2y , y(0) = -5. dx

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Q: 7.Find of z = 2x³-5xy² a²z xy

A: Use partial derivative for finding the unknown

Q: Compute. 13 Σκ k k = 0

A: We have to find out  sum

Q: Evaluate x + 2 S -dx using rationalizing substitution. Which of the following statements is correct?…

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Q: √3.01³ +2.992

A: We need to evaluate :

Q: Question 13 Find the area of the region between the graphs of y=10-2² and y=-3z-30. The area is

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z)=3 ex cos (yz), Po(0,0,0),…

A: Solution: f(x,y,z) =3exCos(yz) P0=(0,0,0)

Q: 5 2 To-4x 1-1/1/2 5-2x (67²) dz dy dx

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Q: Evaluate the double integral over the given region R. S xy cos y dA Sfxy |xy cos y dA= R: -1≤x≤1,…

A: NOTE: Refresh your page if you can't see any equations. . the given integration is  the limits of x…

Q: Which of the following statements is correct to find the volume generated by revolving about x=0,…

A: using shell method formula of area A = 2πy∫abf(y)dy here a = 0 b = 2 A = 2πy∫02 (8-y3)dy so here…

Q: prove that dv v 21/12 الله duz 2 2

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Q: A boy is pushing a box with a force that can be described by the function: (x) = x³ - sin 2x + 1,…

A: Here, given that force can be described by: f(x)=x3-sin 2x+1 And, no other force acting on the box.…

Q: a) pair (4,-6) & (-6,9) b) pair (2,-3,1) & (4,-6,3) c) pair (6,-5,1) & (3,4,2)

A: To determine whether the following pairs of vectors are parallel, perpendicular or neither. a pair…

Q: Find parametric equations for the tangent line to the curve given by x=ln(t+1), y=tcos2t, z=et at…

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Q: Write TRUE or FALSE before each statement. Solve y dependent variable. differential equation.…

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Q: 15. Si dt 1³ + 1² - 2t

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Q: 7.Find of xy of z = 2x³-5xy²

A: To find ∂2z∂x∂y for the given function z=2x3-5xy2

Q: Set up the definite integral required to find the area of the region between the graph of y = 12-2²…

A: we have to find out area

Q: 6e at x-b First find where the two curves meet. y = 5e" meets y = 6e where b Then Area = - f(x) dx…

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Q: Find f'(-1) for f(x) = 2x, Express in exact form?

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Q: 9 B = 10 2 4-[1 ² 3] and 5 6 A = 6. Given EXPLAIN WHY you can multiply AB but cannot multiply BA.

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Q: Sketch the region bounded by the given lines. Then express the region's area as an iterated double…

A: Topic = Area

Q: Verify that * ox af dy 2+ ?х ду ду дх ах 22+ 21 ?х ду ду дж 11 olems) for f(x, y)=5x®y -7xy5.

A: Here is the solution of the given problem.  Partial Derivatives.

Q: Evaluate the following limits: 1-cos¹(x) (i) lim zsin(2x) (ii) lim In (√) +1 2²-1 (iii) lim sin(x) -…

A: Given :limx→01-cos4(x)sin(2x)lim x→1 lnxx2-1lim x→π4 sinx-22cosx-22lim x→01+tan(2x)1x