Example: If ƒ (x + 2π) = ƒ (x), find the Fourier expansion f(x) = eax in the interval [−π,π]

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A: Step 1:Using law of sines we haveba​=sinBsinA​It is given that initially, A=4π​ and…

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Q: Find the general and particular solution. y" + 4y′+ 3y = −e¯*(2+8x), y(0)=1, y'(0) = 2

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Q: 2. Consider the function f : R2 R defined by f(x) = ||x||³, where ||x|| = √√x² + x². (i) Compute the…

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Q: 21/solve the following differential equation Using laplace transform y₁ =-y, Y₁(0)=1 y' = Y Y₂(0)=0…

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Q: 1 1+x 26. Derive the formula: tanhx=-In- 2 1-x ; x<1

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Q: C = (2√3)/3 or (-2√3)/3 within the interval (-2,2)

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Q: Q2. [1 mark] I measure my bike tire pressure at noon, at 1 PM and at 2 PM and the tire pressures are…

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Q: Q3. [5 marks] How long is the shortest ladder that can lean against the wall and clear a 2x1…

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Q: 2sec^2x-2sec^2x•sin^2x-sin^2x-cos^2x=1

A: Step 1:It is needed to prove the following identity:2sec2x−2sec2x.sin2x−sin2x−cos2x=1 Now, the…

Q: 6.2.102. Solve x" — x = (t² − 1)u(t - 1) for initial conditions x(0) = 1, x'(0) = 2 using the…

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Q: Let 4 y = √√x² - 11x+30 x2 dy Find at x = 15. dx dy x=15= dx

A: If you have any help please let me know in comment box thankyou.

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A: We will use the transformation below to transform the equation x2 + y2 = 2 into polar coordinates:x…

Q: I 5. Find the interval of convergence of the following. Be sure to test the endpoints of the…

A: Part a:  We need to find the interval of convergence for the series: ∑k=0∞​k!k2​(x+2)k. To find the…

Q: Use Green's Theorem to evaluate Jc (3y- ) dx + ( 7 x + √y 4 + 1 ) dy (3y-esinx) dx + (7x 2=9 where C…

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Q: Show all steps. Correct answer is 37.6991118

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Q: IV. Consider the equation : y + z = 2. 1. Sketch a portion of the graph of π in the first octant in…

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A: Step 1: Step 2: Step 3: Step 4:

Q: What are the correct answers for the second and third question on this page. I am on the Cartesian…

A: Note :  we have formulas,  a⋅ba×b​=∣a∣⋅∣b∣cosθ=∣a∣⋅∣b∣sinθ​ where, θ is the angle between the two…

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A: Interpreting the Graph and IdeasVelocity: The slope of the position vs. time graph represents…

Q: 2. f(x) = x³-3x² +4 Find all relative extrema, inflection point, and the intervals of concavity 5 3.…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: 2. Find the function f(x) given that f'(x) = 3cos (x) - 2sin(x) and f(π/6)=√3. Leave your answer in…

A: To find the function f(x), we need to integrate f'(x). f′(x)=3cos(x)−2sin(x) Integrating both sides,…

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A: We solve this problem as follows:  Step 1: Define f(x)=3x​Since the derivative of xn is nxn-1, the…

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Q: Please help on all asked questions, Pls show all work and steps, and circle the final answer.

A: ANSWER : ( a ) ​​   ANSWER : ( b ) ​​

Q: π 25. If lies in the interval <0</ and Sinh x = tan 0. Show that: 2 Cosh x= Sec 0, tanh x =Sin 0,…

A: Using the definition of hyperbolic functions, we can show that coshx=secθ, tanhx=sinθ, cothx=cscθ,…

Q: Q6 cons dy= x^" [ x + x^ (1+/mx)/mx] dx Q7) aus. In (cash/ + F Qs) AMS. 252 cosh ++c +A Q₁) aus. e +…

A: It seems you have uploaded answers instead of questions. To assist you effectively, I kindly request…

Q: Please help on all asked questions. Please show all work and steps. Please circle the final answer.

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Q: Find the values of a and b for which each function will be differentiable for all values of x on its…

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Q: chool Which of the following functions describes the graph of g(x)--2√9-x²+37 9 8 7 6 4 2…

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Q: = Q6 What will be the allowable bearing capacity of sand having p = 37° and ydry 19 kN/m³ for (i)…

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