Y Cn) be defined recursively by Let YCO) = 3, Y (1)=4 and Ycn) =3Y(a-1) – 2 Y(n-2) Ynz2. Y (n)= 2^+2 %3D ノ Prove that for all nzl

Q: It is given that 1 (x+3)(x+1) the Fundamental have / 2(x+2) (x+3)²(x+1)² * Theorem of Calculus, we 1…

A: It is given that, 1x+3x+1'=-2x+2x+32x+12. Then, by the Fundamental Theorem of Calculus, we have,…

Q: Cansider h(x)= Ilx? -6x = l|x? calculate Ha) 6 .x T1 3 (22r – 6) A) In(3)- 11 (22.r – 6)3** - (11z²…

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Q: 7x-2 b) xp: 3x-1

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Q: Let f(x, y) = 5e*" and c(t) = (2r², r³). Calculate (f • c)(t). Use the first special case of the…

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Q: If k >= 2 and x in R^ k prove that there exists y in R^ k such that y ne0 but xy = 0 Is this also…

A: If x has any components equal to 0, then y can be taken to have the corresponding components. equal…

Q: 3. Determine a and b for Y X1 and Y2aX bX2 such that EX1 EX2}= 0, Var(X) Var(X2) Var(Yi) Var(2) 1,…

A: The provided information is:

Q: Po fo 22 PE 1(1234)=PP 13)29 pz pz (1432) = p3 p3 pir %3D 12)(34) = E to C13) = pE PE For each…

A: Group D4 is the group of symmetries of the square. Through various rotations, set D4 is formed. In…

Q: The solutions of cosh(2x) = 8sinhx - 5 are a) x = ln (4+ √17) and x = ln (1 + in (1 + √2) b) x = ln…

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Q: Click and drag expressions to show that Ln= fn−1+fn+1 for n=2,3,..., where fn is the nth Fibonacci…

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Q: Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

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Q: a) Get the (2n+1)x Pn (x) = (n +1) Prar tx) +o Pau (x) reconnection polynomials using the; P(x, 2)=…

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Q: Find the residues of the followings functions at z = 0: (1) (z² + 1)/z (2) (z² + 3z – 5)/2³ (3) (2z…

A: 3. Given function is 2z+1zz3-5.

Q: Let Y = Σ(Xi-X)² ~ X² (n-1) Using the TRANSFORMATION THEORY Find the distribution of S²= E(Xi-X)²…

A: Given Information: Consider  Y=∑Xi-X¯2σ2~χn-12

Q: (0 < * < 1) (-1<* < 0) (4) If f(x) = %3D expand f(x) in the form c,P,(x).

A: Give that: f(x)=-12, -1&lt;x&lt;012,0&lt;x&lt;1  Here L=(1+1)/2=1 Fourier  series expansion given by…

Q: Evaluate the Cauchy principal value of 2 x 50% -dx 8 x 2 (x² + 1)²

A: We have to find Cauchy Principal Value of the given integral.

Q: if the Legendre polynomials P.(x) = -1 then: Find 1) ,x* P,(2) dx 2)P'(-1) A) L P.) dx = and P,(1) -…

A:

Q: Find the coefficient of the term containing x' in the expansion of (2x-y)°.

A: Binomial theorem

Q: Let Var(X₁) = Var(X3) = 2, Var(X₂) = 3, Cov(X₁, X₂) = 2, Cov(X2, X3) -2, Cov(X1, X3) = -1. i)…

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Q: (2x + 4) + 1 (2x +4) +1 dx: x2 + 4x + 5 x2 + 2x- 10 2 2 2 Consider dx = x2 (x2 + 4x + 5) dx evaluate…

A: We can solve as follows

Q: show that 11 1+ 1 n-1 1 n(ā-μο)2 Σ=1(xi-x)2 n/2 n(ā – μο)2 Σ=1(α; - z)2 (xi

A: We need to prove that:

Q: Can you show the steps that causes [(1/C)*∫i1dt] to turn into [C*(dV1/dt)] please.

A:

Q: None

A: Given, a)   f(x)=(x-2)2  b)   f(x)=(x-1)(x+1)

Q: Find the artho gon al traje eteries to c°y" - 4y + x*

A:

Q: TIRAT L-1 alo (s²-45-4 (s²+4)² 19129m92 Ilm

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: n² – 1 E(A) Given that Var(R;) = Var(R,) : 12 12n n +1 + 12 E(A) and Cov(R¡, R¡) 12n(n – 1) for i #…

A: By definition, CovaX,bY=abCovX,YCovX+a,Y+b=CovX,Y

Q: Let 6 -2 3 -5 A = -2 and B = 2 -3 (a) Find AB, A-1, and B-1. 14 -24 AB = -4 7 1/2 A-1 %3D 1 3 -3 B-1…

A: We use the general rule for the inverse of a 2×2 matrix and multiplication of matrices to answer the…

Q: Performing iterations on (25) respectively, leads to the following: n-1 X2km+j v; II n-1 Y2km+j…

A: Given: 2km+j=2km+j2+rj To find: Corresponding equation

Q: 21) f(x)=47x A) (4 ln 7)47x Write summation notation for B) (7ln 4)47x x(In 2) C) (In 4) 47x x(In x)…

A: Finding the derivative of f(x)

Q: .3 S(3 – e3*)²dx

A:

Q: Q.4) Find the value of Sigma (d=sum of student id + 22, and c=12) 4c(d + x)(7c* +2cz +9z*) ((d +x)*…

A: As the student ID is not provided, I assume the sum of the digits are 10 (say). Then d=10+22=32 and…

Q: Let X~N (6,2) and P(X>a)= 0,3 Find a?

A: GivenX~N(6,2)Mean(μ)=6standard deviation(σ)=2

Q: (-y dx + xdy) = (a) d(xy) (b) d(y/x) (c) d{ In(xy) } (d) -d(x/y)

A: By quotient rule , duv = v du-u dvv2

Q: The Taylor expansion of f for x→ 10 is f(x) = 10 + 3(x-10)² + 2(x-10)³ + 0((x a) ft (10) = -12 6) fr…

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Q: What is r' (x) when r(x) = In ? Select the correct answer below: O Pu) = - Sr+1 O rw = - Sr+1 x) = !…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.