1. Find the eigenvalues of A and the corresponding eigenvectors. 2. Use the results in 1. above to find the general solution of the system and the particular solution satisfying x (0) = [4]. 3. Analyse the stability and determine the nature of the critical point (0,0).

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Q: 7. Prove: if lim,+ f(x) = L, and lim₂+ g(x) = M, then lim f(x) · g(x) = LM. DE-I

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Q: Consider the SIR model with the square root dynamics dS = A-µS - B√SI, dt B√SI - (+)1, dR = 71-µR,…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: 2. Two fish species z(t) and y(t) are found to co-evolve according to the following model dX = (²32)…

A: We can solve this using given information

Q: Q6: Find the Fourier coefficients and Fourier series of the function f(x) defined by f(x) = { -HAXNO…

A: The given function is                         f(x)=0,   -π<x<0x,       0<x<π   and has…

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Q: V = M2x2 (IR) M = { A€ V A = A²} N = {AEV A = -A^²} Subset V = M let of the vector space V N prove…

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Q: Using the Euler method, obtain the value of y(2) with

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Q: If f(x) = – 1 1 + 8x f'(x) = Σ – Σ n=1 = Σ (-1)"8"an n=0

A: Follow the steps.

Q: et R={(x,y)=R² | x² + y² ≤4y}. Draw it. Write it in polar coordinates.

A: R=x, y∈ℝ2|x2+y2≤4y

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Q: 8. Calculate the following limits. (a) lim (x,y) (0,0) √x - √y+1 xy-1 (x+y+1) (b) √2x-y-2 lim…

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A: Given,Integral,I=∫021xdxTo find: Value of the given integral using any of the numerical methods

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A: According to our guidelines we can answer only one question and rest can be reposted.

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A: To evaluate the definite integral ∫abfxdx, use the following midpoint rule formula.…

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Q: Let f(x) = 3x + 2. Use the € – d definition to prove that lim 3x +2 1. x→1 Definition. E-d proof.

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Q: X X Oml 0 1 4 2 3 9 16 لیا

A: Given data is x 0 1 2 3 y 1 4 9 16   Now forward difference table is x y ∆y ∆2y ∆3y 0 1…

Q: II. Evaluate the following integrals: 1. fe²dx 2. 11 tedx J 1+ 3. fx'e* dx e√x+1 √y +1 4. S dy

A: We have to evaluate the given integrals.

Q: that set of of degree subspace of P₂ Prove or disprove all Spolynomials is 43 not? Or

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Q: 1. Volumes By Slicing. Find the volumes of the solid that lies between planes perpendicular to the…

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Q: Let G(s) = O a. 60 O O O O b. 68 c. 70 d. None e. 64 128 be the Laplace transform of the continuous…

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Q: Find the وه وله dy dx² Please solve in a quarter of an hour please + d9 - 129 - 0 ) ا - (۹۲۰ (0) - 2

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Q: A. Solve the following matrices using the following methods (a) matrix method, (b) determinant…

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Q: 7. Based on the diagram below, find the input string for the output string 011001.(Instruction:…

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Q: Q6: Find the Fourier coefficients and Fourier series of the function f(x) defined by -π<x<0 f(x) =…

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Q: π 1 1 + 2 sin² x dx

A: Consider: ∫0π11+2 sin2x dx Now,  tanx =sinxcosx⇒sinx =tanx cosx⇒sinx =tanxsec x So, ∫0π11+2 sin2x…

Q: Q: Use the Second Derivative Test to classify the local extremes of the function f(x, y) = 10xye-(x²…

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Q: Q6) A-Show that: a) X(f)=X*(-f) 4 To/2 b) if x(t) is even, then b=0, ano/²x(t) cos(2πnfot) dt…

A: Solution : A) a) X(f)=∫-∞∞x(t)e-jftdt X*(f)=∫-∞∞x(t)e-jftdt* X*(f)=∫-∞∞x*(t)ejftdt…

Q: Solve the following differential equations: dy 1.1 (x³ + y²)-(3xy²) X dx [Hint: Let y = vx].

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

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Q: Find area inside 3 - 3 cos 0 and outside r = 3 C

A: Introduction: The polar coordinate system is another coordinate system. In this system, a particle…

Q: Which of the following sets is a basis for P₂? (x² + 3x +5,x²+x+1,3x² + 9x-1) (7x²-x+1,2x²+2x+3,…

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Q: (d) Show that for all integers n > 1 S(n, 1) = 1 = S(n,n), then, using the above relation (or…

A: Solution : Stirling number S, defined by, S(n,k)=1k!∑i=0k-1ikik-in d) S(n,1)=1 Only one way to put n…

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Q: Find the inverse Laplace Transform of 3(S-1) A. 3(cost + sint) B. (S-1)²+1 3s s²-2s+2 C. 3(S-1)…

A: We will use table of Laplace transform