3. Find a power series representation for the function f(x) = = 1 x+2 and find its interval of convergence.

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A: Given that      x = 3t+8  , y = 8t+3

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A: Here, the given parametric equation is: x=2cos(θ), y=2sin(θ), for θ∈[0,2π]

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A: Here is the solution:

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Q: b) 0 em dac

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A: Concept: Area of the square: A=side2 The diagonal of the square is : d=2side Area of circle: A=πr2…

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Q: Evaluate the integral and check your answer by differentiating. x² +8x4 1 x6 1² dx +C

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Q: Use geometry to evaluate the definite integral. 8 26) Evaluate. 27) S 1 S (8 - x) dx x3. + 64 X + 4…

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Q: Consider the following. lim 2x²-3x - 5 x--1 x + 1 Find the limit of the function (if it exists). (If…

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Q: 1. S cosxsin²x V1+sinx dx by algebraic substitution

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Q: (c) Use the ratio test to determine whether the series is absolutely convergent, conditionally…

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Q: 13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3-2 Find an equation for the graph above. 5+ g(u) 4 3 2 - -2- -3-…

A: We need to find equation of given graph.

Q: Given the region D in the first quadrant enclosed by x = 0, x = y², and y = 2. Express D as a region…

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Q: Determine whether yp₂ (x) = x is a particular solution of the following DE or not. y" + 4y = 4x.

A: If yp is a solution of the differential equation f(D)y=Q(x), then yp satisfies the differential…

Q: Consider the following. u = (-7, 3, −2), v = (0, −4, −3) (a) Find the projection of u onto v. 42 25…

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Q: Find f'(x). f(x) = (3x + 10)7 (1 − √) 3(3x + 10) (1 − √x)³ f'(x) = 21(3x + 10)6 (1-√) f'(x) = 7(3x +…

A: Given data÷ fx=3x+1071-x6 Find the first derivative f'x. Useful formula ddxxn=nxn-1…

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Q: dt || y whent = 0, y =

A: Please refer to the image below

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Q: Determine the x- and y-coordinates of the trapezoidal shape. 2.9 b Answers: (x, y) = (i 1.8 b ) b

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. x3 (3x²+2)³ J…

A: Given: I=∫x33x4+23dx     ...1   As we know that; The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: (d) Determine whether the alternating series converges or diverges by using the alternating series…

A: Two tests are done.

Q: Let →r(t)=⟨2t−3,5e^−2t,−2e^2t⟩ Find the line (L) tangent to →r(t)r→(t) t=-3.

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Q: 1- On donne: a- Résoudre l'équation: f(x) = 0 b- Trouver la dérivée : f'(x) c- Calculer: f(In 2) 1-…

A: Given data fx=e2x-3ex where,x∈R We need to solve part a,b,c

Q: 6. g(u) 5 4 3 ANA -4 Based on the graph above, find the following: Amplitude: Period: Midline:…

A: Please see the below picture for detailed solution.

Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

A: Given,           fx=x2-x4 ; x=1To find : Find f'x and find the equation of the tangent line at the…

Q: ⁹1 9x + 7 8x5 dx || +C

A: Given: ∫9x+78x5dx

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Q: 9. Find if x (t) = t + sin(t), and y(t) = t - cos(t). doe

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Q: Find the limit (If It exists). (If an answer does not exist, enter DNE.) (x² - 4x +18, -x² + 4x -…

A: Put the condition for existence of a limit and cross check.

Q: Find the limit. lim (3x-4)

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Q: Engineers and scientists often use visual or mathematical representations to investigate items that…

A: Given :Engineers and Scientists often use visual or mathematical representations to investigate…

Q: Question 1 1 a. [ Use the method of Lagrange multipliers to find the extreme value(s) of f(x, y) =…

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Q: of. F. F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to…

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