2. The subset [a,b) of R is neither open nor closed. Prove it and construc an illustration.

Q: Q.7. y"+6y'+73y = 80e* cos 4x Soln. The general solution is y=Y₁ +Yp The characteristic equation is…

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Q: Find the convergence set of the given power series: (x - 2)n n² n=1 The above series converges for…

A: We use the standard formulas for radius of convergence. The typeset answer is presented below.

Q: Reduce to the form x + yi: logsinh(−i+2) 2 40eni

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Q: Q1: Find partial derivatives of the function with respect with each variable 1) f(x, y)=2x² − 3y – 4…

A: Solution

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 2. lim (√²-x-√x² + x

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Q: GIVEN: L = 1/2 H₂R == 1₁ E=2 I (0)=1 FORM=LQ" +RQ¹ + LQ = E(t) SINCE = I=Q' & I'=Q" THEN LI' + RI =…

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Q: y" ~2y² + 5y = 4e²x cos2x

A: Solution of the non- homogeneous higher order differential equations.

Q: 1. Given the following matrices: 0 11 A = 10 0 1 4- Evaluate a. [(AC) BT] - DT. b. [(BD) TCT]A ¹2 3…

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Q: Q2): A polluted lake has an initial concentration of a bacteria of (1*10' part/m³), while the…

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Q: Explain why the vectors U₁=(3, 8, -8) U₂ = (-12, -32, 32) form a linearly dependent set of vectors…

A: Linearly dependent vectors

Q: O cos 4x + (Dx + E) C) cos 4x + (Dx+ Am Cm 2:

A:

Q: Find the solution of the equation P №²₂ a²z อ + cos y ax² ay ² which tends to zero as x→∞ and has…

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Q: An estimate value of f(x) dx is 10 using trapezoidal 2 - interval rule. W is an estimate value of…

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Q: 1. For the following directed graph, find the shortest path from note 1 to note 9. Please show each…

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Q: Q2): A polluted lake has an initial concentration of a bacteria of (1*10' part/m³), while the…

A:

Q: Write the following English sentences in symbolic form-  I will dance only if you sing. Neither…

A: We can divide the statement into two premises. Let us denote P: I will dance and Q: you sing.

Q: Find the first five non-zero terms of power series centered at x = 0 for the function representation…

A: We have to find the first five non-zero terms of power series representation centered at x = 0 for…

Q: Tickets numbered 1-100 are put into a hat, and four tickets are drawn randomly. Once a ticket is…

A: We want to find true option.

Q: 1.) 4D4 + 20D³ +35D² +25D+6)y=0

A: Given differential equation: 4D4+20D3+35D2+25D+6y=0To find: General solution.

Q: 10. Prove that 7/2 75/2. sin 0 cos (cos a cosec 8) de 10 T 2 (1-cos a).

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Q: Sketch the region bounded by the graph of the equations and find the area of the region. 1 y = y =…

A: To sketch and find the area of the region bounded by the below equations. y=1x2y=0x=1x=5

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 3. lim (x-3) tan(9-x²)…

A: We want to calculate the limit limx→3(x-3)tan(9-x2)sin2(2x-6) To solve this we use the following…

Q: Determine the values of r for which the given differential equation has solutions of the form y = t"…

A:

Q: Example 10.28. Solve the differential equations dz dy = 1 + x2, dx -xy for x = 0.3, dx using fourth…

A: Here, We need to use the fourth-order Runge-Kuta method to solve give differential equations.

Q: Find the solution of the equation P №²₂ a²z อ + cos y ax² ay ² which tends to zero as x→∞ and has…

A:

Q: Example 10.12. Solve the following by Euler's modified method dy = log (x + y), y (0) = 2 dx. at x =…

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Q: Find the area of the region bounded by the graphs of the equations. x-1 y = √x-1, y 2

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Q: Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding…

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Q: Q3): A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a…

A: Newton Method:-  so the value if y at x=5.00 is 6.28 inch

Q: Determine whether the equation is exact. Otherwise, find an integrating factor that will make the DE…

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Q: Consider the plane region to the right. Using trapezoidal rule (2 intervals), Estimate the area of…

A: Solution

Q: H-w.4 Find the volumes for the following solids whose heights are defined by E (x,y) and bases are…

A: Volume bounded by xy-plane plane.

Q: Q2): A polluted lake has an initial concentration of a bacteria of (1*107 part/m³), while the…

A:

Q: QI): The concentration of salt is given as a function of time by: 37.5-3.5x dt at the initial time…

A:

Q: A recent college graduate borrows $150,000 at an interest rate of 6% to purchase a condominium.…

A: Please find step by step solution below:

Q: Find the solution for series solution.) d²y dy 2t + 4y = 0 with the initial conditions y(0) = 1,…

A:

Q: Let B = - {12 31-12-631} and = { · 68} [8] a basis for lower triangular 2 x 2 matrices. (a) Find [[…

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Q: Q3): A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a…

A: Given: x y 2.00 7.2 4.25 7.1 5.25 6.0 7.81 5.0 9.20 3.5 10.60 5.0   To find the…

Q: 4. Find f 6x5-25x4 +8x3+43x²-8x-12 (3x4-11x3 +9x²-11x+6) (9x²+12x+16) Ax+B C(3x+2)+D + x²+1 9x²…

A: Solution using partial fraction method

Q: Given the family C[0, 1] of continuous functions ƒ [0, 1] → R, and the norm ||f|| = sup |f(x)]. x=…

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Q: IV. Find Do not simplify your answers. dx 1. cos x + =xcoshy - 2y, where x > 0 cot ¹(x³) sec³ x 2. y…

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Q: Using two intervals of Simpson's 1/3 rule, an estimate value of f(x) dx is 11.51. The estimate of…

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Q: y = √√²+csc²(πx) 2 COS os(3 cos-¹(x)) - a X

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Q: Q4: Find the derivative of the function at Po in the direction of A 1) f(x, y) = 2xy-3y², P.(5,5), A…

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Q: Find the solution using Variation of parameter. (D²1)y=e* + 1 1 y=C₁e* + C₂e-x+ 를xex ex-1 2 4 1 1 -X…

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Q: Solve using MUC. y" +4y=3sin2x 3+3+5+ y = C₁ cos2x+ C₂sin2x - -Xcos2x 4 y=C₁ cos2x + C₂sin2x +…

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Q: Find the derivatives of the function x²(xy² y)² = x² - y² )

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Q: dy + 4 (X-11² Y = X+1 cos y dx + (x Siny - cos²y) dy = o 0 9. (x-1)³ [X-11³

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Q: ind the function(x), such that f'(x)= In (3x) X ƒ(1)-1. "

A: Function of a variable x

Q: The approximate value of fx sin x dx by combination of Simpson's 1/3 rule and Simpson's 3/8 rule (6…

A: