Use energy method to show that the following PDE p(x)un - [k(x)uz q(a)u, 0 0, u(0, x) = u(0,r) = 0, - 0≤x≤1, u(t,0)= u(t, 1) = 0, t>0 has a unique solution u = 0. Here we assume that p(a) po > 0, k(a)ko > 0, and g(x) > 0. where po and ko are constants.

Q: 4 Which of the following is true for the integral A. In 5-In(-2) B. In 5-In 2 C. -In 5 + In 2 D. In…

A: Solution no. (2)  Options (B) is correct

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Q: Using (a) Jacobi Iterative Method and (b) Gauss-Seidel Method, obtain the solution [12x₂ + 3x₂ −5x₂…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: 1. Let S be the solid of integration of the ff. integral Q. Sketch S and label its boundaries. Q LLL…

A: Solution :-

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A: Solution: From the problem statement, m.v˙+b.v=u  .......i where,           m = mass…

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Q: | Example 8.12. Use the Trapezoidal rule to estimate the integral exª dx taking the number 10…

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Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

A: Solution : Area calculation between the curves, y=x(x-4)(x-6) and y=0 Intercepts of cubic equation…

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Q: 1. Prove that the following functions are quasi-concave: (i) f(x, y) = xy¹, x > 0, y> 0; (ii)…

A: Given: fx,y To find: Quasi-concave function

Q: 鼎 3) Find the derivative f(z) = a) f(z) = 400z(z²-1)" (z²+1) b) f(z) = 400z(z²-1) (2²+1)100 c) f(z)…

A: I just used the chain rule and product rule for derivatives

Q: answer b

A: We will standardized the equation to identify type of surface  and then will draw it

Q: Consider the division of two polynomials: f(x)=(x-c). The result of the synthetic division process…

A: Part (a) We have the coefficients of the dividend are 1  -2   -13   -1  -48 So, the dividend is:…

Q: 2°) Write the volume integral of the solid bounded by Z = √ x² + y²² and Z= √2-x²=y2², in a)…

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Q: Solve the following differential equations: 1. () + (x −2x*)y'+xx=0

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Q: Example 10.26. Using Picard's method, find approximate values of y and z corre- sponding to x = 0.1,…

A: Problem is solved using picard's method.

Q: Consider the differential equation dy = ay - b. dt Find the equilibrium solution ye(t). Ye(t) = |

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Q: 3. Let f [2,3] → {1,3} be a continuous function such that the equation f(x) - x = 0 has a solution a…

A: 3 Give that f:2,3→1,3 be a continuous function such that the equation fx-x=0 has a solution x in…

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A: We have to solve given problems:

Q: dy Example 10.24. If dx mula by calculating y(1), y(2) and y(3) using Euler's modified formula. = 2e…

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Q: a X Q3. Find the edge cover and vertex cover in the graph above G.

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Q: Solve the following system of nonlinear equations 2x₁x₂20 x₁² - 4x₂ - 4 = 0 Using the fixed-point…

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Q: y" + y = tanx

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Q: A 25 C 75 3 ull₂ = 8,ab= 25 then (a + b)2²= B 100 D 50

A: The solution is given as

Q: Directions: Translate each argument into symbolic form (using the suggested letters) and determine…

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Q: Let S be the solid of integration of the given integral Q. (1.) Sketch S and label its boundaries.…

A: From limit of given integral we will find the region bounded and then draw the diagram . While…

Q: Example 10.15. Apply Runge-Kutta fourth order method to find an approximate value of y when x = 0.2…

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Q: 2. Determining whether odd or even function, state the period. a.) b.) .

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Q: 2. Construct the interpolating polynomial of degree 4 using divided difference for the data given…

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Q: (i) Sketch the graph of y = cos x for 0° ≤ x ≤ 360°. On the same axes, sketch the graph of y = cos…

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Q: t if the complex number z is a root of the polynomial f(

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Q: Txample 8.9. Find the maximum and minimum value of y from the following data : =2 0 1 2 4 2 - 0.25 0…

A: Solution

Q: p(1U1) and p((2U2) 1)). 0.11 0.05 0.07 0.08 0.09 0.10 0.20 0.12 0.15 1 0.03

A: Follow the steps.

Q: 1. An indigenous farmer has a 400 feet of fencing and wishes to fence three sides of a rectangular…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

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Q: s+10 B:1: Solve 1. L { t²cosat) 2. L-1{2+₂} (s²-s-2)

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Q: 1. Solid S is bounded by the ff. surfaces. Sketch S and label its boundaries. x = y² + ²-4,…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Graph several level curves for z=2x-y

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Q: 1. Let S be the solid of integration of the ff. integral Q. Sketch S and label its boundaries. 16-22…

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Q: Example Test the canvergence of the following series: { In mo √n h = 4

A: We need to determine whether the given series convergent or divergent. ∑n=4∞ ln(n)n We know series…

Q: 8. Show that for any orthonormal sequence F in a separable Hilbert space H there is a total…

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Q: Find the divergence of = ea + sin(xy) a + cos² (xz) a X O yey+x cos(xy) - 2x cos(xz) sin(xz) ọ xe…

A: U→=exyax+sin(xy)ay+cos2(xz)az

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Q: 2x=4(mod 7) The values of X that makes the statement true is/are Or there’s no solution

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Q: 0 9. f(t)=t-n 0 if t 2π

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Q: 3.2. The least squares solution of smallest norm of th in m x n matrix, is given by

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