b) Show that the ode (x + tan-¹ y) dx + x+y dy = 0 is exact, then find the general solution and 1+y² particular solution if the point (0,0), belongs to the solution.

Q: (c) Evaluate the Riemann integral ₁¹(x) dx by using definition with the parti- tion 2n=1,2}, n+1 =…

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Q: For Matrices AA and AAT find eigenvalues and or the normal eigenvectors when -0. Then find Singular…

A: Given: A=1110   To find: Eigen values and orthonormal eigen vectors of ATA and AAT. To find: The…

Q: Find the amount of each payment to be made into a sinking fund which earns 9% compounded quarterly…

A: Given Data: F.V = $44,000 r=9% =9100=0.09compunded quarterly ⇒m=4rm=0.094=0.0225t=4.5years mt=4 x…

Q: (a) Find the final value of f(t) using the final value property. (b) If the final value is not…

A: Given that Laplace Transform of f(t) is  F(s)=10s+1s2+2 We can write it as…

Q: Find (cost using Laplace find [[ sint] using Laplace

A: Here we can use following formula of Laplace transform 1. Lcosat=ss2+a22. Lsinat=as2+a23. Lftt=∫s∞Fs…

Q: Use the explicit Euler and Runge- Kutta methods to estimate y(2) if y(t) is a solution to y' = 1/…

A: For calculations only take t as x. Given y′=1x2+y, y(0)=1, h=0.2, y(2)=?Here, given is…

Q: (d) Justify whether f(A) compact.

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Q: n For each n EN, consider x == with x ER+. Define the sequence {gn} by x 1 8n(x):= f(xn) (a) Find…

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Q: n For each nEN, consider x = with x ER+. Define the sequence {gn} by x XER+. 8n(x) = f(x) = = (a)…

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Q: Write the first five terms of the sequence. (Assume that n begins with 1.) =3- 5(n 2) a. 22 23 = 24…

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Q: 6. Complete the following for plane with axis intercepts P(3, 0, 0), Q(0, 2, 0), & R(0, 0, 6). A.…

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Q: where co r= Cn Find the solution of x2y" + 5xy' + (4- 4x)y=0, x > - = 1. Enter = 1, 2, 3, ... n =…

A: Given differential equation is x2y''+5xy'+4-4xy=0                    (1)                Suppose,…

Q: Question 1: A risk averse agent, whose utility is given by U(r) = lnr and whose wealth is 50,000 is…

A: Given:  Utility function of risk averse agent is u(x)=ln(x) and wealth is 50,000 is faced with a…

Q: Find BT + BT if B (61 x) =

A: Given B=6-1x   To Find: BT+BT

Q: ocal extremes of f(x,y) = x³ + y² + 3x² - 3y² - 8. A. Calculate second order partial derivatives of…

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Q: Let G be set of all 2 x 2 matrices in GL2 (Z5) of the form (i) Show that G is a subgroup of GL2…

A: Let G be the set of all 2×2 matrices in GL2ℤ5 of the form 10cd, with c, d∈ℤ5 and d≠0.   (i) To Show:…

Q: At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 19 knots and ship…

A: Consider the diagram as per the given situation, At Noon: At 5 PM: The triangle is shown below,…

Q: Find the centroid of a solid that is bounded below by the cone z = x² + y² ㅠ and above by the sphere…

A: Given solid is bounded by z=x2+y2and,x2+y2+z2=z Take in spherical coordinates. The two intersect…

Q: Calculate the area bounded by x (x-4) + y = 0 and the lines x + 2 = 0; y - 4 = 0.

A: We can evaluate the unshaped surfaces by using triple or double integral technique.

Q: Find a basis for the following subspace: W₁ = span{[1, 0,-1, 2], [4, 1, -6, 7], [1, 2, -5, 0], [1,…

A: Given W1=span1,0,-1,2, 4,1,-6,7, 1,2,-5,0, 1,1,-3,1   To Find: A basis for the given subspace.

Q: Suzy Bakery is introducing new cookies and before the cookies can be introduc the activities in the…

A: The arrow diagram is as follows

Q: Consider the set R of 2 × 2 matrices of the form (88) where a, b € R. (a) Show that R is a ring. (b)…

A: Given : R= ab00   ; a ,b ∈ ℝ To Prove : (a)  R is ring .               : (b) R is ring with identity…

Q: Find the closed formula for each of the following sequences (an)n>1 by relating them to a well known…

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Q: 9. In the figure are represented graphically the function y = f(x) and its first and second…

A: 9. To Identify the graphs of the function y=f(x), its first and second derivative from the given…

Q: Let W₁ and W₂ be two subspaces of a finite dimensional vector space V over a field F. 1. Show that…

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Q: n For each nEN, consider x = with x ER+. Define the sequence {gn} by x (a) (b) A = [1,2) CR. (1)…

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Q: Solve the initial value problem with x'(t) = A, for t20 with x(0)= Classify the nature of the origin…

A: Given matrix is A=-1-39-13 We find eigenvalues.…

Q: Let the function f: R → R be defined by 1 x² f(x) = - 0, x = 0, x = 0.

A: Let us solve the given problem on continuity in the next steps.

Q: jw F(w). jw F(W) = jw F(W) = [ [2 - acos (WT) 2 - A Трия cos -2A (₁-COS (NT)) Тјия - 2A (asin ²…

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Q: C: ) Find the value of •∞ 7ln(x) x5 187 Determine whether the series converges or diverges: 7 ln(n)…

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Q: Use mathematical induction to prove the formula for all integers n ≥ 1. 1+ 4 + 7 + 10 + ... + (3n -…

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Q: Find St S 5²425+5

A: We need to evaluate the expression: L-1ss2+2s+5.

Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given…

A: The given matrix is A=   2 -3   1   2-2     0-1   1   3     2   0   4   0 -3   1-2 We have to…

Q: 2. Solve: $1,475 0.06 [(1+0.06) 16

A: We have to find the value of

Q: QUESTION 5 a) Let F(x, y, z)=xyi + (y² + cosz)j + ek where S is the solid bounded by the cone z =…

A: a) Given F⇀x,y,z=xy i⇀+y2+coszj⇀+exyk⇀ So, div F⇀x,y,z=∂∂xxy+∂∂yy2+cosz+∂∂zexy=y+2y+0=3y By…

Q: What is the advantage of including implicit details in a narra O Implicit details require less work…

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Q: (d) (e) (f) -8. Determine the range f(A) where A = (a, 0] for some fixed a < 0,a # Determine the…

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Q: f(x) = x² -5 5 5 X

A: Given function  f(x)=xx2+8 To draw the graph, lets find its properties.

Q: ди Ət 129²u дх2, 0 0 u(0, t) = 1, u(1,t) = 4, t > 0 u(x, 0) = 8x + 8, 0 < x < 1

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Q: (b) (c) Explain the differentiability of f on R by using definition. 1 Let f' be the first…

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Q: Find the y(t) if y(s) = Stl 3-4

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Q: Find the first 10 terms of the sequence an Its 9th term is Its 10th term is 1 an-1 and a₁ = 18.

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Q: Find Imf and Kerf of the following linear maps: a) f(x₁, x₂ + x3) = (x₁ - x₂ + 2x₂) x₁ + x3, x₁ + x₂…

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Q: Consider the conic section given by the polar equation 4 1-sin 0 (a) (b) (c) (d) Without converting…

A: b) Hint: The general form of a polar curve is r=ep1±esinθ,where e is the eccentricity, p is any…

Q: Scenario 1. Your grandparents gave you P 175,000.00 on your 16th birthday. You were instructed to…

A: As per the company guidelines we are allowed to solve one question at a time so i am solving first…

Q: Find the general solution for the second-order differential equation ¨y + 8 ˙y − 9y = −3 with…

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Q: Determine if T (x,y) = (x + y, x - y) is invertable. If so find its inverse.

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Q: Determine whether the following assertions are true or false. If true, prove and if false, explain…

A: Solution:

Q: II. Numerical Methods. Using h = 0.1, approximate the value of y when x = 1.5 for the given…

A: Solution:

Q: a) Use integral test to determine whether the series d dx (tan ¹x) = Hint : 1 x² + 1 k=1 tan k e k²…

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