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Q: sin (2x) dx (x²+L)(x-3) 3) (sin (2x) 88

A: We solve by Contour integration.

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Q: For items 13, 14, and 15, consider the region R bounded by y = Arctan x, r = 1, and the x-axis.…

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Q: Consider the partial differential equation 8²u Du 8x² It' with boundary conditions u(0, t) = 0 and…

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Q: The fifth term of a geometric series is 405 and th sixth term is 1215. Calculate the sum of the…

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Q: ● √3x dy dx √x² + y² So So

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Q: Q2: In usual topological space (R.T), answer the following: 4- Is [0,1] is arcwise in R? Why?

A: Given that ℝ, Tu is usual topological space. To show: 0,1 is arcwise in ℝ.

Q: Show that if a contraction map f: from M to M has a fixed point then it's unique.

A: Definition: Let X, d be a metric space. The map T: X→X is said to be a contraction mapping if there…

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Q: Which interval notation represents -3 ≤x≤3? 1) [-3,3] 2) (-3,3] 3) [-3,3) 4) (-3,3)

A: Here given  -3≤x≤3

Q: 5- Let the dynamical system is given by x=ay-bxy, y = -dx + cxy. The fixed point computed as: (a)…

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Q: calculator?

A: To find the inverse of 3/2 and larger than 1 as,

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Q: 5.2.6 When the matrix of the linear transformation f: R³ → R² with respect to the basis a, ß is 1…

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Q: Given π = (5, 2, 1) + s(− 1, 0, 1) + t(0, 3, 0), the normal of the plane is: a. (- 1, 0, 1) b. (0,…

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Q: 2. Us DI el e6 e7 V3 es V2 es G €2 ez V4 fi W2 WI f2 f3 W3 WA fa G fs f1 W6 W5 f6

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Q: 7. The depth of the water at the end of a pier is 2 m at low tide and 12 m at high tide. There are 6…

A: Given depth of water is 2m at low tide                         &     12m at high tide   Time…

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Q: You are given the equation of three planes which make an inconsistent system. П₁:5x - 3y + 4z - 9 =…

A: Inconsistent are those which does not have any solution . For a system of three variable ( every…

Q: (5) Show that for any real number x and a subset A of R, exactly one of the following holds: (a) x…

A: To prove: If x is any real number and any subset A of ℝ, then either x is an interior point of A or…

Q: A tank originally contains 160 gal of FA

A: Given that a tank initially contains 160 gals of fresh water. Then water holding 14Ib of salt per…

Q: 10 -6 17 The matrix -6 -6 10-3 has eigenvector 10 3 17 -3 37. 1 Enter the corresponding eigenvalue…

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Q: 17. y' + y³ = 0, y(0) = yo

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Q: Given 3 2 SSS 0 0 0 Then, A = Blank 1 and B = Blank 2 C = Blank 3 and D=√4-x² E = Blank 4 and F =…

A: To Change the order of integration from dxdydz to dzdydx

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Q: The equation k₁ d³y k3 dx³ 4 dy ka (de) + k₂y - k5x³ = 0 where ki R, is a third-order homogeneous…

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Q: Determine the amount of a semi-annual coupon and the total coupon paid for a 3% bond with a face…

A: Given: Total coupon is paid for 3% bond value Face value=ℙ 80,000 Maturity at 15 years.

Q: a calculator?

A: To find the inverse of 3/2 and larger than 1 as,

Q: C1. A. 32 B. 234 C. 238 The multiplicative inverse of 177 mod 260 is D. 37 E. does not exist F. none…

A: To find the multiplicative inverse of 177(mod260).

Q: 33. Solve the initial value problem y' = 2 cos 2x/(10+2y), y(0) = nd determine where the solution…

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Q: Consider the autonomous system of non-linear equations * u(, y), where u is a vector field with map…

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

Q: [20 0 -1 1 0 -2 -1] a) Find the characteristic polynomial of A. b) Find the eigenvalues of A. c) For…

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Q: You deposit $100 each month into an account earning 6.3% interest compounded monthly for 30 years.…

A: Here given  Principle amount P=$100 rate r=6.3% time t=30 years,