2 3 1 , V2 = 1 1 Let V1 = , V3 1 > V4 1 -1 [o] 9. t For what value of t is the set {v1, V2, V3, V4} NOT a basis for R*?

Q: II. Consider the sequence (n + 2)! n=1 a.) Show that the given sequence is monotone. b.) Use the…

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Q: Evaluate the Inverse Laplace Transform F(S)=T51)² -2

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Q: Prove that the following limit does not exist: lim (z,9)(0,0) I-y

A: To Prove: lim(x,y)→(0,0)x+yx-y does not exists   Here, we will check the value of the limit along…

Q: Write the integral that would be used to find the area bounded by y =x² + 1, y = x – 2, x = -2 and x…

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Q: 1.Does it follow that if an > 0 for all ne N, thenEn=1 an does not converge conditionally? Explain.…

A: We have to explain the given statement.

Q: 2. Solve the following differential equations: (a) y' e2y = (b) y' = 1+ Y (c) xy' = y(3 – x)

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Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: Eva‎luate the ite‎rated do‎uble integr‎al ∫ 3−1 ∫ 0√(3−y) e12x−x^3 dx dy by chan‎ging the or‎der of…

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Q: Determine whether the following series converge or diverge. (5 – 4(ln n)³)" (V3 . In n)3n 4+ cos? n…

A: Given series are ∑n=1∞4+cos2n3n-n3∑n=1∞5-4lnn3n33·lnn3n

Q: Question 1 Let y be the solution of the Bernoulli differential equation dy = y' +x*, x>0, y >0, y(1)…

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Q: 3- Vn n=1

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Q: 4. Find the volume of solid of revolution (in cubic units) when the area of the region bounded by y…

A: We have to find the volume.

Q: 5. Consider the power series (25 – 1)" a Show that the series is conditionally convergent when z =0.…

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Q: 2. Use the met hod of undet er mined coefficients to solve t he syst em x' = Ax+f, where b. A = f(t)…

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Q: n=1 Vn2 +1 se alternating series test to show that the series is convergent for r = x = 3/8. se…

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Q: Given the matrix G =| 10 5 201 and d, = Then d, and d, are not G- conjugate if d, is given by -1.5]…

A: We know that Two vectors u and v in Rn are A-Conjugate for a matrix A of size n×n if  uTAv = 0…

Q: uppose an individual wants to have exactly $300,000 available for her child's education. (a) Find…

A: The formula for the amount compounded continuously is given by  A=Pert where A is the amount  P is…

Q: Determine whether the following series converge or diverge. 4+ cos? n (5 – 4(In n)³)" Σ | 3n – yn…

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Q: Q5) Find volume of body bounded by z = x-y from below and z = x+y from Above inside y = x ,y 2.

A: Volume bounded by the region

Q: Find the sum of the following convergent series. 3n+1 1 6n-1 n=0 'n + 1 n=16

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Q: The base of a solid is the region enclosed by the graph of y = vln x, the line x = e, and the…

A: Given,  The base of solid is the region enclosed by y=ln(x), the line x=e and the x-axis. Also…

Q: 4. У(п) %3D [x1(п) * х2(п)] х1(п) %3D 26(п) + 56(n-2) х2(п) 3D 46(n-4)

A: Given y(n)=x1(n)*x2(n) Where x1(n)=2δ(n)+5δ(n-2)                (1) x2(n)=4δ(n-4)…

Q: Σ -1)2n Find a power series representation for (2n)! It is known that for all x ER, cos x = n=0 +00…

A: This is a problem of Taylor series.

Q: If C is the circle |z|=4 evaluate Sf(z)dz for each of the following functions using residue. (a)f(2)…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: А - (BUC) — | (А — В) UC (А — В) U (A — С) | О Оption 4 Оption 1 (А — В)n (A — С) (А — В — С)

A: 1. As by distributive property A - (B ∪ C) = (A - B) ∪ (A - C) Hence Answer: Option 1 (A - B) ∪ (A -…

Q: Find the particular solution of

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Q: Petermine whether the following series is convergent or divergent (-1)"3n² 4n²–1 (b) n=1

A: Given series is ∑n=1∞(-1)n3n24n2-1

Q: Given de - and dy = . Then do and dq are not G- conjugate if G is Non of these 12 O A 0.5 0.25] [18…

A: We want to find matrix for which vectors are G conjugate

Q: (-1)" Consider the series expansion of the cosine function cos(x) = )) -x2n for all x € R. (2n)! n=0…

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Q: Let [7 -37 A = -4 -1 -6 -2 7 -7 a Define the linear transformation T : R³ → R³ by T(ã) = Aã. Find…

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Q: 10 You have carried out an experiment to investigate the effect of the length of a pendulum on the…

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Q: Q4) Find plane area inside the polar function r = 2 and outside the polar function sin ( - 0) +1 in…

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Q: Really hoping for solutions since I’m having a hard time with this. Pls. skip if unsure or not…

A: Given question is Let f (x, y) = ln(2x3 − y2) − 4xcos(y − 1) + y a. Fin‎‎d the loc‎‎al linea‎r…

Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: Let T: R? R² be a linear transformation that sends the vector u = (5, 2) into (2, 1) and maps v =…

A: To find the value of the given linear transformations .

Q: dy dv S.S; as sin ny dedy Cii)

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Q: IV. Determine if the given is convergent or divergent. sin(2 tan¬1 n – 1) #3. )) (2 tan-1 n – T) n=1

A: Given series is ∑n=1∞sin(2tan-1n-π)(2tan-1n-π)

Q: If ffinite or in finite) Contable set, thers prave that At CS}=0

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Q: Q2) Solve the D.E xdy + (2y-x*+ 3x)dx 0 %3D

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Q: 2s - 1 s2 - s -- 2' F(s) = s2 – 4 - 4 F(s) : (s2 + 4)2 1 F(s) = s2 + 3s + 2

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Q: Find out if the improper integral converges or diverges. If the given converges, find its value.…

A: Solution

Q: Find whether the shown expression below diverges or converges Show your solution and how you came up…

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Q: Use the algorithm for finding A to find the inverses of the matrices shown to the right. Let A be…

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Q: 1 + 4 = 5 2 + 5 = 12 3 + 6 = 21 8 + 11 = ?

A: Solution :  Given that  1 + 4 = 5  2 + 5 = 10  3 + 6 = 21  8 + 11 = ?

Q: 2. Use the met hod of undet er mined coefficients to solve t he syst em x' = Ax+f, where - -] b. A =…

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Q: Q4) Find plane area inside the polar function r = 2 and outside the polar function r = sin +1 in…

A: Here we use double integration to find the area.

Q: 2. Use integration by parts to evaluate the following. (a) Sx tan-1 x dx

A: Given integral is ∫xtan-1 x dx

Q: 4 - 2v2. R

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Q: Let S be the su‎rface with eq‎uation ->R(u, v) = 〈2u sin v, 3u, 2u cos v〉, whe‎re 1 ≤ u ≤ 4 and 0 ≤…

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Q: Determine whether the alternating series £ (-1)n+1, n3 converges or diverges. n= 1

A: Given alternating series is  ∑n=1∞-1n+13nn3