Example 19,9. Show that the equation of the ellipse having foci at z, z, and major axis 2a, is |2 -z,1 12 - z| = 2a. Also find its eccentricity.

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

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Q: 2. (a) Find the exact length of the curve (i) r = 1+sin 0, 0<0< 27, (ii) r = 2(1+ sin 0), 0 <0< 27.…

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Q: Given the differential equation y"+ 5y' – 5y = 0, y(0) = - 1, y'(0) = 2 Apply the Laplace Transform…

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Q: Suppose that dP/dt = 0.19P(t) represents a mathematical model for the growth of a certain cell…

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Q: 23. -(-Cnd)→e -evd dz

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Q: Find the inverse Laplace transform of the following functions: (a) F(s) = 38+6 %3D s2+3s' (b) F(s) =…

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Q: Solve the equation: u = a u 0 Uxx u(x, 0) = f(x), a(0, t) = u(L, t) = 0 %3D

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Q: Use X = eAtC to find the general solution of the given system. %3D 0 0 0 X' =5 0 0X 7 10 X(t) = %3D

A: We will find eigen values and corresponding eigen vectors  of the equation to get general solution

Q: Graph the following make sure to label all asymptotes, end behavior, x and y intercepts, and holes!…

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Q: yA C(0, 1) B(1, 1) y=Vx R2 R3 R y x' A(1, 0) Referring to the figure above, find the volume…

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Q: using the derivative test. c) i) Find the Taylor series for c(r, y) = sin(r + 2y) and d(r, y) = In(+…

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Q: Use cylindrical coordinates. Evaluate the integral, where E is enclosed by the paraboloid z = 7 + x…

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Q: let fo) - X In (x) , using the following approximation formula for the secowd denvative 1. assuming…

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Q: Recall that X = 0(t)-1(to)X, + (t) -(s)F(s) ds solves the initial value problem X' = AX + F(t), X(t)…

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Q: Solve the following Initial Value Problem using Laplace transform: y" - 6y'+ 5y = e¯ 10 t ; y (0) =…

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Q: The function 1. f(z, y) 4+4x + 4y can be expressed as a Taylor Series about z = 4. y - 5 ie. 1 f(z,…

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Q: 6. Evaluate ž dz, where ti-clockwise din (b) C is the semicircle z = 2 + 3i + 5e", 3 4T in the…

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Q: Let A be an m xn matrix over R. We define NA := {x € R" : Ax = 0}. %3D NA is called the kernel of A…

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Q: 2. Let Ax = b be a system of linear equations in variables. Designate the columns of A as a, a, a,…

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Q: Using the Alternating Series Remainder Theorem, determine the number of terms N required to…

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Q: Let A, B be 2 x 2 matrices, C a 3 x 3 matrix and D a 1 × 1 matrix. Find the condition on these…

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Q: State and prove the base case State the inductive hypothesis Outline how the rest of the proof…

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Q: a If f is an odd function, why is f(x) dx = 0? a Choose the correct answer below. O A. a a a Since f…

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Q: , Prove that if A is an all-zero matrix for some k > 1, then 0 is the only eigenvalue of A.

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Q: Find |[F•N dS (flux), where F(x, y,z)= 4x'zi +4y'zj+3z*k, S is the sphere with radius R centered at…

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Q: Complete the following payroll ledger. Find the total gross earnings for each employee. Time and a…

A: For BianchiHours Worked -         46.5Reg. Hrs. -                  40 (Given)O.T. Hrs -…

Q: The function (z, v) – 4+4z +4y can be expressed as a Taylor Series about z 4. y-5 ie. f(z, y) + a(z…

A: Taylor polynomial of a function f(x,y) for at the  point (a,b) Where  first and second partials…

Q: The total forces acting on a object falling through Earth's atmosphere is given by the differe…

A: The given differential equation is  mdvdt=mg−kv

Q: Consider the following graph. If b is the source vertex, what is the minimum cost to reach f vertex?…

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Q: Using the Alternating Series Remainder Theorem, determine the number of terms N required to appro…

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Q: Find the partial sum S17 for the arithmetic sequence with a = 2, d = 5. S17 Question Help: D Video

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Q: Determine the inverse Laplace transform for the following. s – 1 2s2 + s + 6

A: HERE WE USE SOME FRACTIONS AND BASIC OF LAPLACE TRANSFORMATION

Q: Find the eigenvalues and eigenvectors of the matrix 8 B

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Q: x 0 1 2 3 4 f(x) 8 8.8 9.68 10.648 11.7128 decide whether the function f(x) could be a linear or…

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Q: How quickly can you find the eigenvalues of an upper triangular matrix?

A: We have to say that in how quickly we can find the eigenvalues of an upper triangular matrix.

Q: Iffis continuous and f(x) < 0 for all xE[a,b], then what is true about f(x) dx? a Choose the correct…

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Q: of of and dy For the function f(x,y) = 7x* – 7y-2, find of of %3D ду

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Q: x² ( e 15y – 1) + 3 (y- 5x²) ² 84 + 7y? +7 (y - 5x2)? Let f(x,y) = Find f(x.y). (x.y)-(0,0) lim (a)…

A: Given function is fx,y=x2e15y−1+3y−5x228x4+7y2+7y−5x22. a We have to evaluate limx,y→0,0fx,y along…

Q: Colour shades judged by Consumers. A firm not sure of the response to its product in ten different…

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Q: Solve the following application problems. 3. Judy Martinez is paid $34,060 annually. Find the…

A: Judy Martinez is Paid $ 34060 annually We need to find equivalent earnings if this amount is paid…

Q: ez Write the adjacency matrix for the graph. Write the incidence matrix for the graph. State the…

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Q: Diagonalizing a Matrix In Exercises 7-14, for each matrix A, find (if possible) a nonsingular matrix…

A: The given matrix is A=2-2   30   3-20-1   2 We have to find a nonsingular matrix P such that P-1AP…

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: Solution:

Q: Match each of the power series below with the correct statement about it. Series A: +1 n=0 Series B:…

A: This question related to power series .

Q: Is it the case that for propositions p, q and r, (p → q) + ((p V r) (q V r))?

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Q: 2. Let S = {vi, v2, V3} be a set of linearly dependent vectors in an inner product space V. What is…

A: To explain: What will be the result when we apply Gram-Schmidt process to a linearly dependent set…

Q: on to 6- The map T: F F[x]/f) defined by r(x) = x + (S) = [x] is an epimorphism. This map is called…

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Q: For the directed graph depicted below do the following (a) find the adjacency matrix (b) find the…

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Q: 7. When 3 edges are removed from a graph G without removing any vertices the resulting graph G' is a…

A: Given: 3 edges are removed from a graph G without removing any vertices resulting in a graph G'…

Q: For the following exercises, find rectangular coordinates for the given point in polar coordinates.…

A: To conversation from polar to rectangular coordinates is given by : x=rcos(theta) y=rsin(theta)