Determine whether the series Σ (-1)" -5 In n n=2 converges absolutely or converge conditionally. (Hint: Use alternating series test, limit comparison test and p-test)

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Q: Prove that if a and b are both positive, and a2 < b2 then a < b          (Use Indirect Proof)

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Q: Which of the following statements is always true about real m-by-n linear system, where m

A: We have to find out which of the following is true for the given statement.

Q: 3. Let An, A, Bn, B be subsets of 2. Show lim sup A, U Bn = lim sup A, U lim sup Bn. n-00 n-00 If A,…

A: 3) let An , A , Bn , B be the subsets of Ω show that limn→∞supAn∪Bn=limn→∞sup An ∪limn→∞supBn if…

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Q: 2.59 Find || f |sup if a) f(x) = x on (-1, ). So if x E Q, b) f(x) = – x² .2 if x ¢ Q. -

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A: Given: Let us consider the given, The area enclosed Fx=x13,y=2 and the y-axis. and consider the…

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A: Consider the given function fx,y=e−x2−y2cosxy. We have to determine the first and second degree…

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A: Let us solve the problem in the next step.

Q: 1.10.6 Show, by expansion of the surface integral, that S, do x V lim = V x V. sdt-0 fdr Hint.…

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Q: Assume that G is a non-abelian simple group and that |G| < 168. Prove that G = A5.

A: Sol

Q: Starting with Poisson equation, derive the inequality that defines the sheath edge: -> 9s dv dz

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A: We have find magnitude of the resultant force.

Q: 2- Solve the problem 0<t< 00 P.D.E. u = Uxx + sin(nx) Su(0, t) = 0 lu(1, t) = 0 u(x,0) = 1 0 <x<1…

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Q: Rule 1: Multiply by 2 then add 1 starting from 1. Rule 2: Divide by 2 then add 4 starting from 40.…

A: To find the ordered pair of sequence 1 and sequence 2 given in rule 1 and rule 2 respectively .

Q: Find the laplace transform of F(t)= 2t^4-3e^2t+10sin3t

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A: Sol

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Q: a) Find the directional derivative of f(x, y,z) =xy-yz'+z at the point P= (1,-2, 0) in the direction…

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A: Y=4-984261-25X=1-3-74261-25 Y is obtained from X as shown below.

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Q: Let S be the upper half of the unit sphere x +y +=1 and take n as the upper unit normal. Use Stokes'…

A: Stokes theorem is used to find out the integration

Q: 3 1 2 3 2 Из Suppose that the CTMC models an M/M/1/3 queue. What are µ2 and u3?

A: Sol

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Q: Draw a first order predicate logic proposition for the sentence “Everyone who works hard in CST 3170…

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Q: Consider the function defined by f(x, y) = 4x² + y². (a) Find the domain and range of f. (b) Draw a…

A: The given function is f(x,y)=4x2+y2, (a) To find: The domain and range of f. (b) To draw: contour…

Q: Prove that matrix Y is obtained from matrix X. Identify the property of determinants and prove |Y| =…

A: 2. Given  Y=4-984261-25 X=1-3-74261-25 We will prove that matrix Y is obtained from matrix X.

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A: This is a problem of sequence.

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A: Consider the given function fx,y=e−x2−y2cosxy. We have to determine the first and second degree…

Q: Q2) Solve the following simultaneous equations using Gauss elimination method 2x + 3y + = 13 x- y-…

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Q: cosh In(-3+2j)] a. -1.6154 + 0.9231j b. 1.9396 + 0.0741j c. 18.3972 + 0.8193 d-15.3227 10.1998j

A: option a is the correct answer

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A: We can solve this using formula of fit straight line, standard deviation, standard error ,…

Q: (с)(2у) dx + (6x3— ху — х)dy 3D0

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Q: 5 How many isomorphisms are there between the following two graphs? Explain. (If you do not know…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

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Q: (In3+j5)5 sech(5.5430°) tanh j 4 V[ej – j213 ji]4 Evaluate the function above. Key in your answer in…

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A: We will find integral of both sides of strokes theorem with given range of variable . Integral of…

Q: choose the appropriate answer.

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Q: -3 8. Let v = 2 and ts be given vectors in R. Which of the following vectors is a linear combination…

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A: Given vectors:v1=1-320, v2=025-4 and v3=12-21 be given vectors in ℝ4.We have to check which of the…

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A: The given equation is dθdt=λ120-θ,         θ≤100°. In the given equation, dθdt is the rate of…

Q: (a) |V(G)| > a(G) · w(G) (b) |V(G)| = a(G) · w(G) (c) |V(G)| < a(G) - w(G)

A: This is a problem of Graph Theory.

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A: We have to solve this using rule of inference.

Q: 26. If z = In(x² +y²), find x- ду Əx A) х с) у в) х-у D) 0

A: If z=ln(x2+y2), We need to find x∂z∂y-y∂z∂x.

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Q: d(x) = 5x(t 2d(t) %3D

A: Sol