Suppose ƒ and g are continuous at a. Prove the following using e-d arguments. (a) fg is continuous at a.

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A: By using  , we will find the series solution of the given differential equation.

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Q: Consider the following initial value problem. 0 1 ≤1 12 1 ≤ 1 < 6 0 6 ≤ 1< 00 y' + 3y = y(0) = 10…

A: The Laplace transform of a function f(t) is defined as L{f(t)}=∫0∞f(t)e−stdt .Formulas: (1)…

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A: One must not assume f(c)= 0.But If one assumes that , then the claim "" is true.

Q: Let fig: DR be continuous at ce D. Prove that fg is continuous at c.

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Q: Use de Moivre's Theorem to find the following. Write your answer in standard form. (√2 cis 77)

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Q: True or false: The series Σ n=1 a. true b. false (-1)"+¹ n 62 +4 converges.

A: We have to check the convergence of the series .

Q: The three series Σ An Σ Bn, and Σ Cn have terms 1 n7 2. EMBIMBiM8 3. Σ An Use the Limit Comparison…

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Q: Use simplex method to solve the following Linear Programming (LP) problem. Maximize Z=4X₁ +8X₂ +6X3…

A: Maximize Subject toWe have to solve the LPP using simplex method.

Q: Find the following limit. √√x-4√√x 8%√x+4√√x lim 8118 lim 8118 5√x-4√x 8√x +4√x (Simplify your…

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Q: Problem 2 . Let M(d) be the set of all matrices with the size d x d, where d E N and d≥ 2. (a)…

A: Given Information:The set is the collection of all matrices with the size .To show:a)  if  are…

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A: r(t)=(e2t, 2e2t , 2e6t)Find r'(t)Find T(t)

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A: A graph of the tent is given, the aim is to find the amount of material needed to make the tent.

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Q: 0.3 +0.03 +0.003 +0.0003 + ... (a) Express the series in the form M8 n=1 an (b) Does this series…

A: Series   0.3+0.03+0.003+0.0003+........general form of geometric progression terms is…

Q: The system of first order differential equations y₁ = 5y₁ + 1y2 32 y₂ = −4y₁ + 1y2 where y₁ (0)= 4,…

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A: We compute the flux of the vector field through the surface.

Q: Find the volume of the upper region cut from the solid sphere rho <= 1 by the cone phi = pi / 3

A: We have to find the volume of the upper region cut from the solid sphere ρ≤ 1 by the cone  ϕ= π3

Q: Prove that the d₁ ("Manhattan") metric on R2 is really a metric.

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Q: The general solution of the homogeneous differential equation associated with the equation…

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Q: ) Determine the set of all optimal solutions for the following linear program using the graphical…

A: To solve the LPP in graphical method, we have to convert it into dual problem.

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Q: Consider the following matrix: 1 2 3 0 -3 A-3 6 -9 09 -2 5-9 -29 Give a basis for each of im(A) and…

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Q: Find the Maclaurin series for f(x) = 1/(6-x-x2) and determine its radius of convergence. You must…

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Q: Evaluate f(V x F) dS where S is the surface x² + y² +3z² = 1, z ≤0 and F = (y, -x, zx³y²). Let the…

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Q: Explain the integral obtained in Green's theorem of a vector field F(x,y)=-(1y/2)i + (1x/2)j that…

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Q: Let f : R → R and ECR. Prove f is continuous iff f-¹(E) is closed whenever ECR is closed.

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Q: 2 east one of the answers above is NOT correct. e ite the given third order linear equation as an…

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Q: 1: Consider the following differential equation, 5xy"' + (2 + x) y + y = 0. Note that xo = 0 is a…

A: is a regular point.

Q: Use simplex method to solve the following Linear Programming (LP) problem. Maximize Z=4X₁ +8X₂ +6X3…

A: First two constraints are less than type so adding slack variables s1,s2 with these constraints.…

Q: 2. Let S denote the surface of the cube [0, 2] x [0, 2] x [0, 2], but with a small square removed,…

A: Let  denote  the surface of  the  cube but with a small  square removed, the  square with corners…

Q: Part II. Writing the equation d² dt2 in the form of the system dx d dt (c) (d) (e) = V, = x³ + x², X…

A: To solve part(d) , we need part(a),(b),(c) , that's why I am solving first four parts.