1. Use the Euler, improved Euler and Runge-kutta methods to solve the following ODES:

Q: me that tu Su lve the follawis Apply Jucobi's equations 3x+24=4-s 2x+3y=Z=5 yu=1-6 %3D

A: Given equations are 3x + 2y - 0z = 4.52x + 3y - z = 50x - y + 2z = -0.5

Q: Assume that u E W%3 (R"). What is the largest q such that we can guarantee that u E Lº (Rº). O 30 7 ...

A: In this question, 3 is the largest q such that we can guarantee that u∈Lq(R10). Hence option third i...

Q: Give 2 examples of Continuity and Discontinuity. Show your complete solution using the three conditi...

A: We know that a function fx is continuous at a point x=a if limx→a- fx=limx→a+ fx=fa, where limx→a- f...

Q: Find the Laplace transform of sin t cos t

A: Given f(t) = sin t cos t = 2sintcost2 = sin(2t)2

Q: Use the direct methods to Solve the fellowny systems of algeboriac equations Xi + X2+ X3 + X4 = 3 2X...

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Q: 00 (2х+3)" 2 2n+n-1 n=1

A: Given series is ∑n=1∞(2x+3)n2n2+n-1

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to y or x. ...

A: Let us consider the curve y=f(x) and y=g(x) the area under the curve y=f(x) and y=g(x) between the i...

Q: Apply Gauss-Seidal method to sulve the fotlowing Lineur equativns 5 X-2 X z =18 -2XI + lo X2 -2X3=-6...

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Q: NO. 5 Jenny Company produces two types of pants: long pants and short pants. The cost of making a pa...

A: let the number of short pants be x let the number of long pants be y as given  cost of making pair o...

Q: The plane passing through the three points A(0, 1,3), B(3,4,3) and C(2,3, –1) can be expressed as a ...

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is...

A: The vector that passes through the points: Ax1, y1, z1 and Bx2, y2, z2 is defined as AB→=x2-x1i+y2-y...

Q: 2. Let the rref of a matrix A be, (1 0 0 1 2 0 -2 -5 0 -3 0 0 1 6. Determine A if the first, second ...

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Q: What are the Euler equations associated with the Lagrangian L(x, Y, Y' , z, z') = (y')²z – 3xz'y O 3...

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Q: the first derivative of a continuous function y=f(x) is y'=x(x-12)^2 .find y'' and then use the grap...

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Q: f: {0, 1}4 → {0, 1}3 f(x) is obtained by removing the last two bits from x and adding a 1 to the end...

A: We want to find image of f(0000).

Q: A coin is tossed three times. Let H and T be the head and tail shown on the side of the coin facing ...

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Q: 3) Let r(x) = 2x2 Sketch the graphs of the functions in the same xy-plane in the following steps. x²...

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Q: Find the sum of the series S.

A: Given,         3-3ln(2)+3(ln(2))22!-3(ln(2))33!+ . . .

Q: Determine from the graph whether the function has any absolute extreme values on [a, b]. Then explai...

A: For given graph, Absolute Maximum is at x = d. and  Absolute minimum does not exist.  

Q: Define the binary operation in the set of rational numbers as: a*b=ab+a- b Which of the following pr...

A: Group theory  

Q: Question 1 State the order and linearity of the following differential equations cos(x*y) y" + 5xy'-...

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Q: a b c a b c If def=2, find the determinant of g hi g hi de f The determinant is

A: The solution is given as  

Q: OUse the direct methods to Solve the followry systems of algebriac equatons 4X - 3y +57= 34 X = 4 2X...

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Q: ELEMENTARY APPLICATIONS OF DIFFERENTIAL EQUATIONS (GROWTH AND DECAY METHOD) Jun has decided to save...

A: Introduction: The exponential growth and decay model is useful in calculating the amount related to ...

Q: Let (Ti+1 – x)³ P:(x) = a;- hị (r – x;)3 + ai+1 + b:(xi+1 – x) + c;(x – x;). hị for i 1,...,n – 1. S...

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Q: Determine the rank and nullity of the matrix. 2 -1 0 1 5 2 1 -4 -1 -4 -1 6 -8 -5 -2 9 The rank of th...

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Q: Find the singular value decompostion of the matrix -1 1 1 -1 1 1

A: Given: 1-11-1-11

Q: Find the determinant by row reduction to echelon form. 1 -1 -2 0 3 -2 3 2 1 3 2 3 - 1 5 6 3 Use row ...

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Q: Let X be an ordered set, and A C X. Show that a. for every E X, x has at most one immidiate successo...

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Q: Problem 4: (Finding and using Taylor series) 1 to show that the Taylor series centered at a = 0 for ...

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Q: State the order and linearity of the following differential equations i) cos(x?y) y" + 5xy' - 18y = ...

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Q: Apply Gauss- seidal method to sulve the fotlowing fottowing Lineor Lineur equations 5 X-2 Xz -2X1+lo...

A: Let x1 = a, x2 = b, x3 = c So given equations are5a - 2b = 18-2a + 10b - 2c = -60-2b + 15c = 128

Q: Let (x) = x*(x - 1). (a) Find the critical numbers of the function f. (Enter your answers from small...

A: It is given that ;                     fx = x4x-13   ................(I) (a) We have to find the cri...

Q: 2: Change the order of integration. •ln 4 f(u, у)dydx.

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Q: 5. Consider the equation f(x) = x - 2- = 0. (a) Show that the above equation has a solution on the i...

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Q: EVALUATE and FIND THE REAL AND IMAGINARY PART OF THE GIVEN EQUATION. Given: A = 8 – 2i B = 4e¬i C = ...

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Q: Activity 2: Let students to answer this activity in order to connect the next topic. Solve the first...

A: Properties of the derivative ddx(uv)=udvdx+vdudxddxxn=nxn-1ddxf(g(x))=f'(g(x)) ddxg(x)ddxsinx=cosxdd...

Q: If a = i+ 3j +k and b = i+ 9j + k, find a unit vector with positive first coordinate orthogonal to b...

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Q: 4. Consider the weighted voting system [14: 14, 10, 2, 1]. a. What is the quota? b. How many players...

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Q: Question 3 Captain Picard and the rest of the crew of the Rocinante are defending their position on ...

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Q: OUse the direct methoeds to Solve twe fullown systems of algebriac equatons 4X - 3y +5Z = 34 2X-y-Z ...

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Q: Use the 2016 FICA tax rates, shown below, to answer the following question. If a taxpayer is not sel...

A: The expression: "x% of y" is same as the expression: x100×y. Calculate the tax corresponding to the ...

Q: Can an (6,4)-graph is connected.

A: (6, 4) graph has 6 vertices and 4 edges. Now, any graph with n vertices will be connected if there i...

Q: Salve the fullowing equations using bisectrion thed me X siAx+CusX= fors] Xost

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Q: let f:(a,b)→R be de fined by XƐQN(a,b) 2 f(x)=' 3 xƐQ'N(a,b) show that dif ferentable on f? why?

A: This is a problem of Differential Calculus.

Q: For the function:     F(x) = x3/3 – 3/4x2 – 27/2x +39 (i) Determine the coordinates of the turni...

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Q: Find an equation of the tangent line to the graph of g(x) =2-x² at the point (2,0). Write the equati...

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Q: 1 -2 3 Let A = -6 12 Choose the true statement. 2 6 -8] Select one or more: O The rank of A is equal...

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Q: Assume that SN is a bounded C™ domain ofR° and that u E H™ (N). What is the smallest integer m such ...

A: In this question, 5 will be the smallest integer m such that we can guarantee that u is continuous. ...

Q: Compute the flux of the vector field i = -2i+ j- 2 k through the rectangular region shown below, ass...

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