Use the transformation u =x + 2y, v=y-x to evaluate the given integral by first writing it as an integral over a region G in the uv-plane. 1 3-2y || (x+2y) e -) dx dy , (y – y

Q: Q/ Choose the right answer y" + 6y"+ 11y' + 6y = cos(x) +e^{-x}

A: To find the general solution of the following differential equation.y'''+6y''+11y'+6y=cos x+e-x

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Q: Consider a nonhomogeneous differential equation y" + 4y = -12x + 10e. (a) Verify that yp = -3x + 2e*…

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Q: Find any critical numbers for f and then use the second derivative test to decide whether the…

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Q: For items 1 to 5, consider this function: 3. y = V5x² – 4 y%3D

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Q: 16 in. 12 in. A 18 in. mLA = 38.95 mZB = 123.04 mZC = 18

A: Given

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Q: 5 (5y, + 1.5y)3 16.036 (5 + 2/3.25y.) INIM

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Q: 2. ASSume that 9 (x)= 4X-1 of sOme unction gX) the intervaS on which the or.ginal function, 9X), is…

A: Here, the given that the function g(x) has the derivative: g'(x)=4x-1x23

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Q: 10. Related Rates d. The area of a circle is expanding at a rate of 10 cm? per second. How fast is…

A: Note that the area of the circle is given by: A=πr2 Differentiating it with respect to t:…

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Q: A note card company has found that the marginal cost per card of producing x note cards is given by…

A: Given : Marginal cost in cents is C'(x)=-0.08x+75    , for x≤1000   To Find : Total cost for…

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A: Since the student has posted multiple questions and has mentioned to solve question numbers 6-10,…

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Q: 16 14 12 10 8. 6. 4. 6. A942

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A: Let the numbers are x and y  x=7y Sum of the numbers(S) = x + y S = x + y S = 7y+ y Differentiate…

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Q: The graph of the function f(x) 1. x+ 6 + 13 is a transformation of the graph of the function 9(x) =…

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A: Given query is to find the direction derivative.

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Q: Trigonometric Groups 3. S sin³x cos5xdx 4. S Vtan x sec*x dx

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Q: 2. Find the equation of the tangent line to the graph of y = 3cos 4x at x = 3

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Q: J (3vx +) dx = *+ 3) +° si- dx = In\xl - e* + C 3. 4. E. x2 %3D (鼎) 「(回-dx=n F. 2V 5. S 2+3* dx = 4…

A: Note:- As per your demand we solve question 4,5,6 for you  Given problems:-

Q: [1] What is the c value of a parabola with a Vertex of (4,2) and a Focus of (4,4)?

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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Q: Find the quotient and remainder on dividing:  8x^3 + 12x^2 + 1 by 2x + 3

A: Given query is to the quotient and remainder.

Q: Do not use a calculator in this question. 3 V3 6+2v3 5- V3 p+qV3 6. find the CS CamScanner value of…

A: This question is based on similar parallelogram properties and rationalisation.

Q: Find the area of the shaded region. f(x) = x – 8x° + 21x, g(x) = 20x + 50 3

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Q: N(N+1) N(N+1)(2N+1) N (N+1)? Use linearity and the formulas Ej = E = and Σ"- to evaluate the sum. 4…

A: ∑j=0 46j(j-1)=∑j=0 46 j2-j=∑j=0 46 j2-j  =∑j=0 46 j2-∑j=0 46 j

Q: The outline of a rugby ball has the shape of + = 1. The ball itself is the y2 30 16 revolution of…

A: I am attaching image so that you understand each and every step.

Q: 3. Find the derivative of the following functions using differentiation rules. x2+V+V+14 a. y = b. y…

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Q: ind the integration below: of the last two digits of y

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Q: buff'g'sinay olxly

A: To solve the following integral

Q: Find the Taylor series of f(x) = 1 centered at c = 3. %3D Choose the Taylor series. 2-1)" *- 3)n+1…

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Q: Find a power series representation for the function. (Give your power series representation centered…

A: We will use binomial theorem for the expansion of the function.

Q: (0.7)

A: Let's find.

Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

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Q: Fill in the table and then sketch the vector field. z| y F(z, y) = (, %3D 20 0 2 -2 -2 2 -2 -2| -2 2…

A: Here, to fill the table and then plot the vector filed.

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = x°y*2? . F(1, Y, 2) =

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 5y2 + 4, (3, 4) %3! Vf(3, 4) =…

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Q: COLUMN A COLUMN B S(:-0) dx =-4 In\x| + C 4 In/x| + C 1. A. 4x B. 4* 2. dx 6Vx +C С. 4 3. S(3Vx +)…

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