Expand f(x) = 4x² + 10x + 10 as a power series around x = -1. f(x) = (x + 1)² + (x + 1) +

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A: Given: z=xyx-yWe need find zxy.

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A: Since you have posted multiple questions i can do first question as per our company guidelines…

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Q: Σ(51) k

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A: The given function is ; f(x)=3x2(x-1) 7.

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A: The given data is: sech-114 Evaluate  sech-114

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Q: 1. fx³ex/²dx

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A: Please see the below picture for detailed solution .

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Q: 7. Find d when 5x² +3x³y -3y³ = 44. Write an equation of the tangent line at the point (2,2).

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A: Given: m(t) = 490e-0.03t, where m(t) is mass remaining after t years. To find: a) Mass at time t = 0…

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Q: Evaluate the integral 8√√2 S 0 25 ds 256-s

A: The definite integral is ∫08225256-s2ds To evaluate: The value of the definite integral. Formula…

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Q: ja √√₁²-y² Va2-22 -√a²-y²-√√a²-x² - y² √√a²-x²-y² α ,2 2 ,2 (x²z+y²z+z³) dzdxdy

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Q: Find the critical point of the function: f(x, y) = -1- 6x-2x² - 5y + 3y² (x,y)= This critical point…

A: f(x,y)=-1-6x-2x2-5y+3y2for critical points put ∂f∂x=0∂f∂y=0∂ ∂x(xn)=nxn-1∂ ∂x(constant)=0

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A: Here we have to choose the correct option.

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A: We will find the required.

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A: Given: Find the general solution to the system x'= Ax, where  A=1-51-3

Q: 1 Evaluate the following definite integral. √51² (i) cos x sinx dx; (ii) [₁ xv1+r² dr. VT

A: (1)  (i) G=∫0π2cosxsin4xdx∫xndx=xn+1n+1+c

Q: 1. Set up (evaluate later as an exercise) the integral ſſ(2x − y)dA by changing to polar…

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Q: Express the number as a ratio of integers. 0.59 = 0.59595959... Need Help? Submit Answer Read It…

A: The objective is to express the number as a ratio of integers .

Q: Which of the following is equivalent to 3x²(-2x)e-x² + e-x²16x O -16xe-x²(x² - 1) O 16xe-x²(x² + 1)…

A: Given query is to simplify the expression.

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Q: . Find the centroid of the plane region bounded by the graphs y = 2³ and 2 = y².

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A: Here we have to observe the graph.

Q: Find all the rational zeros. Write the answer in exact form. q(x)=−4x^4+5x^3+7x^2-10x+2

A: Given that q(x)=−4x^4+5x^3+7x^2-10x+2 Since all coefficients are integers, we can apply the rational…

Q: x²-4x+3 1. Compute limx→3 x-3 Oo 01 02 03 ONone of these

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Q: Solve the system of linear equations. -3x + 2z = -14 x + 4z = -14 -x - 2y + 3z = -10 O (2, -2,-4) O…

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Q: Evaluate the integral √2 S s² + √5 2 ds

A: Use the Sum Rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1   To evaluate the…

Q: 78. GEOMETRY CONNECTION Part of the three- dimensional mathematical figure called the horn of…

A: According to our guidelines , we can answer only first question. Kindly re-post other remaining…

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A: Given:-The height of rocket ht=2t2