In the name of god 1.Use taylor series method to get solution to dy dx -=x+2y-xy, y(0) = 1 1) Find taylor expansion (at least 5 terms) 2) Find y at x=0.1 and x=0.5

Q: III. Find the determinants of the following matrices using Laplace Expansion and Triangular matrices…

A: Given matrix is C = -2    7  0   6-2  1-1  3   2   2  3   4  0   5   3  2   5-4-2   2  0   3-1   1…

Q: Determine by inspection whether the given set of vectors is linearly dependent or independent. Do…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: Given the function 4s-8s2+ss2+1 make the partial fraction as follows 4s-8s2+ss2+1=4s-8ss+1s2+1…

Q: Let u and v be two vectors for which ||u||²+ ||v||² = ||u+v||²

A: Given that ||u||2+||v||2=||u+v||2 consider the right hand side |u+v||2=u+v.u+v

Q: Find the coefficient of a-2 in the binomial expansion of  (27a2 - (1/81a3))9

A: Let us consider the expansion x+yn The binomial expansion is obtained as x+yn=∑k=0nCknxn-kyn

Q: H 6 and let W be the set of all x in R3 such that u x = 0. (a) Show that W is a subspace of R³. (b)…

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Q: 5. Let P([0, 1]) be the space of polynomials on [0, 1] with the norm of uniform convergence, that…

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Q: Find the total degree of the graph. 10 07 O 20 CO 8

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Q: 2. Simplify completely: (a) √1+i√3 (b) (2 + 3i)¹+i

A: 2. To Simplify: (a) 1+i35 (b) 2+3i1+i

Q: Find the eigenvalues and eigenvectors for A = The eigenvalue a + bi = The eigenvalue a - bi = 15…

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Q: Answer true or false. F(s) = s²/(s² + 4) is not the Laplace transform of a function that is…

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Q: Let A and be any sets. Mark the statement that is true OAUB CA OA - B C В В СВ O AC = { } = OANB C в

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Q: (a) The eigenspaces of a matrix A are shown in the figure below. Find A (3). 2-eigenspace Y x…

A: Note:- As per our guidelines and due to time limit, we can solve the first part only as exactly one…

Q: Solve the initial value problem O O O y = 3test = est = est + est 3e5t + 3e5t y = test O y = 3e5t y″…

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Q: 3. (a). Use Laplace transforms and partial fractions to solve y" +4y=8t, y(0)=3, y'(0) = 0.

A: Given  y''+4y=8t, y0=3, y'0=0

Q: Suppose {u, } form an orthogonal basis in R2 and y = 2ū - 7 where u = (8) 6 If W = Span{}, what is…

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Q: Given the triangle below, find the following: Note: picture is NOT drawn to scale. Round all answers…

A: Given that: Angle A = 29o Angle B = 21o Side b = 28   So, applying sine rule: asin A = bsin B = csin…

Q: n (c) Find a vector b in R³ such that the solution set of Ax = b is a line in R³ parallel to the…

A: Introduction: Only when there is a 0 degree angle between two vectors can it be said that they are…

Q: We prove the following statement using element proof and contradiction. For all sets B and C, (B-C)…

A: To prove the following statement using element proof and contradiction. For all sets B and C, (B -…

Q: during typhoo Ambo, PAGASA tracks the amount of accumulating rainfall. For the first three hours of…

A: For first three hours, the rain fell at a rate of 25 mm per hour.  So for time 1≤t≤3 the rate was 25…

Q: 7.) Write the System System of Tinear equations augmented the variables Jose if applicable…

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Q: 10. (True/False) Suppose D is a region where any two points in D can be joined by a curve that stays…

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Q: Prove that the function ƒ : (0, ∞) → R defined by ƒ(x) = x³/² = (√x)³ is not uniformly continuous.…

A: To Prove: The function f:0, ∞→ℝ defined by fx=x3/2=x3 is not uniformly continuous. To Use the…

Q: Consider the statement: Vrational numbers r and s, r/s is rational. The statement is true. We can…

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Q: Q1. Find the derivative of the following functions. a) G(x) = ²3 et -dt et + b). H(x) = plnx ² +1 14…

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Q: has its largest value. a = Find two numbers a and b with a ≤ b such that b = # (10 + 3x - x²) ¹/³ dx

A: We need to determine: a, b such that ∫ab10+3x-x213dx is maximum.  Here, a≤b.

Q: ( The discriminant fxx fyy-fy is zero at the origin for each of the following functions, so the…

A: Given that the discriminant fxxfyy−fxy2 is zero at the origin for each of the given function. a…

Q: You deposit $1,000 in an account at the Lifelong Trust Savings and Loan that pays 4% interest…

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Q: Solve the following inequality algebraically. Include an interval chart in your solution.  5x+4x-11…

A: The solution for the given inequality is x∈(-∞,2411) or x<24/11

Q: For any integers m and n, if m mod 11 is 6 and n mod 11 is 7, what is m+n mod 11? 13 9 42

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Q: Find two numbers a and b with a ≤ b such that has its largest value. 1/3 (10 + 3x -x²) ¹/³ dx

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Q: The inverse forms of the results in Problem 49 in Exercises 7.1 are and s-a y(t) = .(sa)² + b² } -3t…

A: The solution is given as

Q: Consider the following matrix: A = 2000 0200 -302 3 300-1 a) Find the distinct eigenvalues of A,…

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Q: Evaluate ** Vx2 + y2 dydr. .

A: We can find the value of the integral by converting it to polar coordinates using the following…

Q: The temperature of a point is given by T(x, y) = x+y. Calculate the average temperature of the…

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Q: ● If the pollution index of a point (x, y) is given by p(x, y) = x². Calculate the total pollution…

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Q: Fill in the blank. (Enter your answer in terms of t.) 1 1 (S-2) 6 < =

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Q: Show your work. Simplify your results. Find the best fit line y = mx + k for the following points…

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Q: The vector field F = (y², 2xy + e³2, 3ye³z + x) is conservative

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Q: B. Test the divergence of the following series n=1 n

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Q: Consider the following function. f(t) 1 1 (3, 6) Use Definition 7.1.1, to find L{f(t)}. (Write your…

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Q: 1. For the integral fff 6(x, y, z) dV where E is bounded by y = z², z = 0, y + 2z = 4 express it as…

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Q: Calculate the present value PV (in dollars) of an investment that will be worth $1,000 at the stated…

A: The future value of the investment is $1000 Time is 11 years rate of interest = 6.7% per year…

Q: Let D(0,1) = {z : |z| < 1}. Suppose there is a function f : D(0,1) → C such that f(1/²) = i/n² for…

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Q: Solve the initial value problem 0 y = 2e-2t +e-21 O y = cost + 2sint O y = O y = O y = e 2¹ cost +…

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Q: Consider the following initial-value problem. y' - y = 2 cos(7t), y(0) = 0 Find {f(t)} for f(t) = 2…

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Q: What method do we use to prove the statement: Vinteger n, 5" - 1 is divisible by 4. Direct proof…

A: We use Mathematical Induction. Let's start For n = 1   5 -1 = 4 is divisible by 4. It is true for n…

Q: 2. At what point does g(x) == have a removable discontinuity? A. x=8 B. x= -8 C. Nowhere D. x = 1 E.…

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Q: Let V₁, V2, and v3 be vectors in a vector space V, and let T:V → R³ be a linear transformation for…

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Q: n! > 2^n for all n> n0. Make a table to compute the value of n0.

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