Suppose a function f(x) = x between 0 and 1, and f(x) = 0 elsewhere. Solve for the fourier transform g(k) of the original function f(x).

Q: Use the second Taylor polynomial for f(x) = cos (x) at x = 3л to estimate cos (1 + 3л). Round your…

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Q: A window has the shape of á parabola above and a circular arc below. Find the area of the window…

A: To find: The distance from the x-axis to the top of the circle. Write the equation of the circle.…

Q: { ∞ ^ > ㅣ 8. Determin S 9"+5 S

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Q: The set of polynomials {3t²-3t+5, mt+6t²+10} is a linearly dependent set in P, if 2 m=6 Select one:…

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Q: Define a binary relation =3 on Z by x=3 y if x - y is divisible by 3. 1. Prove that 3 is an…

A: There is a relation on Z such that x is related to y if (x - y) is divisible by 3. Our aim is to…

Q: If S= √√√3-1 2√2 √√3+1] 2√2 √√√3-1 2√2 A √√3+1 2√2 P = S (adj.A) ST, then find matrix ST p¹0 S. and

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Q: lim x--7+ dx [oo] f. dx [[ f(x)dx g. f(x)dx h. Average value of f on [-4,-1]

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Q: Use the Generalized Principle of Inclusion and Exclusion to find the number nonnegative integer…

A: Given: The given equation is x1+x2+x3+x4+x5=28. To find: We have to find the number of non-negative…

Q: Explain why lim F(x) in Figure A exists, but lim f(x) in Figure B does not. X→2 X→-2 -6 Since lim…

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Q: d) Has it been translated left or right? If so, by how much? e) Graph. Your graph must have a scale…

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Q: For each of the following series, determine whether the series converges, diverges to ±∞, or…

A: We have been given the following series: i. ∑n=1∞sin23n+22n2-3 ii. ∑n=1∞1n-2π iii. ∑n=1∞n+1n3+2 We…

Q: Given: A = [1 3 3 202 € M3 33 (a) Find the eigenvalues of A and determine their algebraic…

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Q: (c) Find a power series representation for fx arctan(x) dx. You can use the sigma notation or the…

A: Here we use series for arctan x. Also in the last question we use Taylor error approximation.

Q: Use cylindrical coordinates to evaluate SG √x²++y² dV, where G is the solid above z = 9 - x² - y²…

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Q: ²+ b² + c²p²-2(ab + bc+c

A: Part a

Q: A function f(x) is defined by a0 f(x+=)=f(x). Obtain the Fourier series to represent the function.

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Q: respectively

A: Part a

Q: 2a₂b₁ Let A = ab₂ + a₂b₁ a₁b3 + a3b₁ a₁b₂+ a₂b₁ 2a₂b₂ a3b₂+ a₂b3 a₁b3 +azb a₂b3+a3b₂. Expressing…

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Q: 1 a 1 b C f(a) (x-a) 1 f(b) (x-b) f(c) (x-c)| a² bb² a с f(x) (x-a)(x-b)(x-c)

A: we expand the left side determinants.

Q: 2. Show that 27 |(5²2-4).

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Q: Prove using mathematical induction. Show your solution. Prove 3 + 7 + 11 + … + (4n – 1) = n(2n + 1)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Determine whether the following series converges or diverges. Be sure to state why it converges or…

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Q: Ifx +2y+32 = x2 + 2y2 + 3z2 = x² + 2y3 + 3z3 = 2, and xx +2y2y3 +3z₂Z3 = x3x₁ +2y3v₁ +3Z3Z1 = x₁x₂ +…

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Q: Find the gradient vector field of the function f(x, y) = x - 2y + 5 Problem 1. and sketch this…

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Q: Answer the following questions about the equation 1 4x³ − y² + ²⁄yz² − x(y − x)e² +1=0. (1) Does the…

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Q: Given the two vectors -9 -5, and = V2 -3 -20 -5 -11 Choose a vector v so that the set {V₁, V2²…

A: The given vectors in ℝ3 are  v1=-9-5-3, and v2=-25-5. We have to find the vector v in ℝ3 such that…

Q: If f+g is are differentiable at x0, then prove f and g differentiable at x0 ww

A: We are given that the function (f+g) is differentiable at x0. one has to show that f and g both will…

Q: Find the area of the shaded region. Round your answer to three decimal places. 0.3 06 A 0.2 $ -0.8…

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Q: EXTRA CREDIT Find the total area between the graph of f(x) = x² – 11x + 24 and the x-axis on the…

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Q: WORK PROBLEMS (6 Question 1 a) i b) c) s): You must provide a clear and detailed solution for each…

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Q: SOLVE STEP BY STEP IN DIGITAL FORMAT Problem 8 Determine the linearization of f(x)=√1 + 3x at a=0.…

A: The Linearization of a function y=f(x) at point x=a is given by…

Q: Using mathematical induction, show your solutions to prove that  1 + 5 + 9 + ... + (4n-3) = 2n^2 -…

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Q: Prove if the following system is linear or not? d² x dx d²y 3 dt² dt² dt + 4y = -4- +3 - ×IN 2

A: A system of differential equation is called linear if the power of derivative and dependent variable…

Q: Question 1 Given the differential equation 3y" − 21y' + 36y = 3e-4² a) Classify the given…

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Q: Determine which theorem applies to simplify the following. It is possible that more than one will…

A: Given  Find the work done by the vector field Fx,y,z=yzcosxyi^+xzcosxyj^+sinxyk^ along the…

Q: DIRECTIONS: PROVE THE FOLLOWING VIA MATHEMATICAL INDUCTION. SHOW YOUR SOLUTIONS. 1. Prove 6 + 4 is…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Given the linear transformation defined by T(x) = Ax and A a. Ker(7) b. Nullity(7) c. Range(7) d.…

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Q: In order to sketch the graph of f'(x), we must have a formula for f(x). O True O False

A: False.   See Explanation in step-2.

Q: are in A.P., b, c, d are in G.P. and at a, c, e are in G.P. -10 - e

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Q: Give a solved problem on Volumes of solids of revolution using Circular Disk Method. Show complete…

A: Circular disk method is also known as disk washer method.Answer given below

Q: 4. What is the equation of the line that passes thru (4,0) and is parallel to the line x-y-2 = 0.

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Q: f(x) = 3 tan x. (a) Solve f(x) = -3. (b) For what values of x is f(x) < -3 on the interval π π…

A: (a) Let, f(x)=3tan(x) Now, f(x)=-3⇒3tanx=-3⇒tanx=-1⇒tanx=-tanπ4⇒tanx=tannπ-π4⇒x=nπ-π4where…

Q: Problem: A tank contains 20 kg of salt dissolved in 5000 L of water. Brine that contains 0.03 kg of…

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Q: 6.Find half-range Fourier cosine series for f(x)=x in (0<x<2π)

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Q: (3) If {f} converges uniformly converges uniformly on [a, b]. on (a, b) and {fn(a)} and {fn(b)}…

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Q: where A = Ife is defined ase=I+A+ *].0<x< , 0<x< 1 and I is identity matrix, then find the functions…

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Q: If A 0 " P= [13] AP= PA, then what is A¹⁰ ?

A: Given: A=5-230, P=1213 To find: A10.

Q: Determine whether each of the following series are absolutely convergent, conditionally convergent,…

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Q: Evaluate the integral SF ds, where F(x, y, z) = (x, y, 1) and 5 is the upper hemisphere of the unit…

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Q: Find the flux of the field F(x,y,z)=z¹ i+xj- 6z k outward through the surface cut from the parabolic…

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