Determine whether or not the vector field is conservative F(x,y) = 18x²y²i + 12x³yj conservative O not conservative

Q: Consider the function f(x, y) = y ln x - x ln y - . a Find the directional derivative of f at the…

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Q: The subset in the form [3]. Select one: O TER and y = -x. O None of these O r = -y and y ≤ 0. Or#0…

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Q: lo 12-dxdy = (1 2* dx) (ody) Select one: O True O False

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Q: The function f(x, y) = 2x³ - 6x + 6xy² has: Select one: O One minimum One maxima and one saddle…

A: Topic:- application of derivatives Note :- as per our guideline if more than one question uploaded…

Q: Solve the problem. 28) A kitchen remodeling company determines that the marginal cost, in dollars…

A: In this question we have to find the cost of installing an extra 9 feet of countertop.

Q: Question ( correct for the series 3): Which of the following is n=1 Select one: O equals. O equals…

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Q: y=x²+2x when x=2 and Ax=0.05

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Q: Q1 (2 Let R be the region bounded by y = 0, y = x², x = 1. a) [ 1 Sketch the region R. b) Evaluate…

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Q: Evaluate the integral and check your answer by differen NOTE: Enter the exact answer. [x x(7+x²) dx…

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Q: The function f(x, y) = 5 - 3x² + y² + 7y + x has: Select one: O A. None of the others B. One…

A: fx,y=5-3x2+y2+7y+x We have to find how many critical points this function has.

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. [t√4 t√4t² +…

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Q: Suppose (2, -1) is a critical point of a function f with the continuous second derivatives. If fxx…

A: We need to choose correct option.

Q: Suppose (1, -1) is a critical point of a function f with the continuous second derivatives. If fxx…

A: As we know from the double differentiability test, When rt-s2>0 and r>0 then minima will…

Q: 3) A) E B) [ Consider the homogeneous DE: y'"" + 2y" + y = 0 Verify that y = cos(x) is a solution of…

A: The given differential equation is;  y''''+2y''+y=0

Q: 1₂x (x + y) dA, where R is the region that lies to the right of the y-axis between the circles x² +…

A: We have to evaluate the integral.

Q: Use the double integration find the area of the parallelogram whose vertices are A(1,0), B(3,1),…

A: Area of parallelogram

Q: Let f be a function defined for t≥ 0. Then the integral is said to be the Laplace transform of f,…

A: The given function, ft=-1,0≤t<11,t≥1

Q: Which of the following functions is symmetric about the y-axis? f(x) = x2 f(x) = x3

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Q: Solve the length of the unknown side. Round each answer to the nearest tenth. 21 La ins 120000 2…

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Q: The directional derivative of a differentiable function f(x, y) in the direction of a unit vector u…

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Q: The Integral f fyr² dyda can be written as: Select one: ọ Sổ Sing dady O None of the others Of fyr²…

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Q: Find c if a=3mi, b=3.5 mi and ∠C=40.2degrees. c=   mi;

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Q: (9x - 8) dx || +C

A: Solution of given question is written in below steps.

Q: Which of the following is the directional derivative of f(x, y) = 2xy² - x³y at the point (1, 1) in…

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Q: 2- Évaluer les intégrales suivantes: a = √ x√x + 5 x ₁² dx x2 2- Evaluate the following integrals:…

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Q: What is the value of the integral Select one: O 64 O 16 O None of these O 32 08 0 X 2xydydx?

A: Given: I=∫04∫x42xydydx   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: Consider the following vector field F(x, y) = Mi + Nj. F(x, y) = x²i + yj (a) Show that F is…

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Q: 14. Determine whether the triangles are similar. If they are, write a similarity statement. Explain…

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Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) =…

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Q: Find an equation for the ellipse whose graph is shown. y 0 (10,5) 15 X

A: Consider the ellipse  Consider the graph

Q: Determine whether the equality is true or false 2 4 4 √₁² √ ^ (x² + y²³ dxdy = √(√² √2²day) +…

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Q: A triangular parcel of land has sides of lengths 330 feet, 650 feet and 732 feet. a) What is the…

A: We can answer both the question as below.

Q: please both

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Q: Solve the given initial-value problem. dx dt dy = 25x - y dt x(1) = 0, y(1) = 1 x(t) = 0 = -11x - y…

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Q: The Integral fi fig(z,y) dyda can be written as: 21-9(x,y) dzdy Select one: O True O False

A: We can solve this as follows:

Q: Find the absolute maximum and absolute minimum values of the function, if they exist, over the…

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Q: The value of the integral is equal to: Select one: None of them 813113 L. (8 (8x - 8y) dy dx

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Q: 4. Determing whether the following series are absolutely convergent, conditionally convergent, or…

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Q: Classify the following diferential equations. Write the order, linearity and the homogeneity of the…

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Q: Find the relative extrema of the function, if they exist. 3) f(x)= 3x4 + 16x3 + 24x2 + 32 4) f(x) =…

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Q: Use LaGrange multipliers to find the minimum distance between the origin and the plane x+2y+3z=28.

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Q: Q1 (2 Let R be the region bounded by y = 0, y = x², x = 1. a) [ 1 Sketch the region R. b) Evaluate…

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Q: The value of the integral is equal to: Select one: O 4 O с صرا من م من ته 3 x ²² (4x - 4y) dy dx

A: The given integral is: I=∫01∫0x4x-4ydydx   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: 6. Find the area of one loop of the polar curve r = 2 sin 30

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Q: Using Trapezoidal method [√x dx for n = 4 is equal to 0 Blank 1 (use 2 decimal places with proper…

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Q: Find an equation for the hyperbola that satisfies the given conditions. Asymptotes: y = x, hyperbola…

A: To find an equation for the hyperbola that satisfies the given conditions.Asymptotes: y=±x,…

Q: Obtain an exponential function in the form f(t) = Aert. HINT [See Example 5.] f(t) is the value…

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Q: 1a) Convert the Cartesian equation (x^2 +y^2-1)^2 +4y^2-1 = 0 to polar coordinates. 1b) Use a…

A: By using the following substitution we can convert the Cartesian equation to polar form. x²+y²=r²…

Q: Find the absolute maximum and absolute minimum values of the function, if they exist, on the…

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