Expand the function f(x) = x² - 2x + 1 in the interval [ -1, 1] using Fourier series formula.

Q: smallest to largest x, then from smallest to largest y.) x' xy - 4y - 5 y = y²x² smaller x-value X…

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Q: Given Taylor polynomial is pn(x) =

A: Given the Taylor polynomial is                       pn(x)=∑j=1n(-1)j-1j(x-1)j

Q: Q4: Discuss the Continuity of following Also find at x = 1 range. and x = 0. Sxx+1 3x+5 -2 -2x+1…

A: a Given function is fx=x+1,    −2≤x<−1x,            −1≤x<03x+5,      0≤x≤2 We have to check…

Q: Classify (if possible) each critical point of the given second-order differential equation as a…

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Q: Q2/ Use the mid-ordinate rule with eight intervals, to evaluate 23sin² (x), correct to 3 decimal…

A: The mid-ordinate rule uses the midpoints of the subintervals to approximate an integral. The…

Q: Classify the critical point (0, 0) of the plane autonomous system corresponding to the nonlinear…

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Q: Find the root of equation  X^3-x^2+2sinx=0 By using N-R method.

A: Newton Raphson Method xn+1=xn-f(xn)f'(xn)

Q: e2-s L-1 = s(s-3) O [(-1/3)+e^(3(1-1))/3] e^2 U(t-1) O [(-1/3)+e^(5(1-1))/3] e^2 U(t-1) O…

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Q: The auxiliary equation of the differential equation -5y""+y' + 2y = 0 is -5m³ + m² +2m = 0. O False…

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Q: ax Q2. Fit the following data by the equation y = b+x X 3 6 Y 20 40 using the Least squares method 9…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: find soot by using

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Q: nk 2j ΣΣΣ - k=4j=7h=6 first step 2nd step 3rd step 4th step

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Q: 5. (*) Let V be a vector space over F and let U be a subspace of V. Define a relation ~on V by…

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Q: Integrate the following functions f(x) = 4/2/201 22²2 + + [2,³] X 3 x

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Q: Consider the function f(x) = 4x Identify the locations where f has transition points. (Give your…

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Q: The value of a collectible toy is increasing exponentially. The

A: Given the collectible toy is increased exponentially. The two points on the graph show the toy's…

Q: = Exercise 0.3.23. (a) Prove that the function f(x) vex over [0, ∞). (b) Prove that for any a₁, A2,…

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Q: A given partial fraction 2x (x-1) (x+4) (x2²+1) A x-1 + B x +4 + Cx+D x² +1

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Q: 3) L¹{e 2. ₂2}

A: We have to find the inverse Laplace transform of the function F(s)=e-2s·1s-2 i.e. ℒ-1e-2s·1s-2

Q: 3. f(x) = ln(3x - 4) - cos x; f'(5)

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Q: 1. Given a two variables function z = f(x, y) = √√√36 - 4x² — y². (i) Determine the domain and range…

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Q: ing La 15. y' + 3y = t, = { 0, 0≤t≤2, t> 2 y (0) = 0

A: As per our company guidelines we are supposed to answer only the first question. Kindly re post the…

Q: answer each question by true or false and explain 1) L{t * e³t} = L{te³t} 2) L-¹{L{t* et}} = t * e³t

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Q: Solve for all values of x over the interval [0,2m]: 2sin(x)=sin(2x)

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Q: 5 Solve your given pair of complex numbers placing them on an Argand diagram. A=2+13 B=3+1/2 C=3-12…

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Q: dx de X = X(t) defined implicitly by 62 +62 V X In(t) = ext. Also evaluate dx at dt (tox) = (1,1).

A: Given 62+62xlnt=e62xt

Q: A student wanted to find the value of factor A experimentally in the equation F-9.2Av². If the…

A: Given the equation is F=9.2Av2 and the student plotted the values of F on the y-axis and the values…

Q: Consider a large vat containing sugar water that is to be made into soft drinks (see figure below).…

A: (A) Frame the differential equation as per the given situation.

Q: In Exercises 5 and 6, the polygons are similar. Find the ratio (red to blue) of their perimeters and…

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Q: ■) Prove that 3 (2+1 +5") for every integer n ≥ 1.

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Q: A particle is moving along the x-axis so that at any time t > 0, its acceleration is given by the…

A: The acceleration of a particle is the rate of changing of velocity at time. When the velocity…

Q: A function is given by x - ex = 0. Find the root between a = 0 and b = 1 by using Bisection method.…

A: Bisection Method Concept If f(x) = 0 is given equation and a, b ∈ℝ are the roots (assumed) such that…

Q: Fill in the blanks in the following: 1. If a =(3,-2, 6) and 5=(4,-1,-6) the axb=........ - 2. If a =…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: (3) Verify the identity: 1+cos + 1-cose 2csc²x

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Q: ind the sum of the following convergent series. lim 348 lim 348 lim 11 Σ [tan" (2n-1) - tan^³ (2n+…

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Q: y" + xy' + (x2 + 2)y=0

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Q: د و ولد 6 -1) ze

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Q: d the lower and u

A: Given,        2x3-15x2+36x

Q: dx = -.5x + 2y dt dy = .4x - 4y dt Solve for x(t) and y(t) given the initial conditions stated…

A: given equations dxdt=-0.5x+0.2ydydt=0.4x-0.4y with initial condition x0=50y0=70

Q: L-¹ 1 {3²-45+8}

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Q: sequence an = an−1+ an-2 and a₁ = 3, a₂ = 4, ; For the its first term is its second term is its…

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Q: Consider the function f(n) = 2[n/2] from Z to Z. Is this function one-to-one? Is this function onto?…

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Q: Plot the following curves in polar coordinates. 4. r r = sin() 5. r= 1 + cos 50 6. r² - sin 0

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Q: On Thursday, it is Reeta's turn to walk. Peter drops Nikita off at a certain point leaving her to…

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Q: The inverse image of the disk | z |< under T(z)=is z+1

A: You will find solutions in next step

Q: 5) t2 * e3t S²¹e²-¹² di

A: Convolution: The Convolution of two functions f(t) and g(t) over a finite range [0,t] is given by…

Q: (6) Let f(a), g(n) € Pla] where f(a) is irreducible.

A: Let m = deg(f(x)) and n = deg(h(x)).

Q: :) = { = k₁ f(x) = -2<x<0 0<x<2

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Q: e²-s L-1 - 3) O [(-1/3)+e^(3(t-1))/3] e^2 U(t-1) O [(-1/3)+e^(5(t-1))/3] e^2 U(t-1)…

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Q: d, d': xxx-R be two metrices on x that Satisfy following for every nEX and >0 7>0 st. Bai (x, S) C…

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