3x Given f (x,y) =4e* In y with x = In (u cos t) and y = u sin t. The correct value of dz evaluated at (u ,t) =| V2, ди is given by 4 A. 42. 3 O B. 2 V7. O C. 2.

Q: a Write down the derivative of arcsinx. b Use integration by parts to find | arcsinx d.x.

A: a. Derivative of arcsin(x) is given by ddx(arcsin(x)) = ddx(sin-1(x)) = 11 - x2

Q: [2 - 3 2 - 3 and be express as A = LU as below L4 – 1 - 2 1 c) Let A = |1 | 01 [u11 U12 U13 [2 - 3 2…

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Q: Use the Gauss-Seidel method to find approximate solutions to -21 + 3x2 + 23 = 5 2x1 + 2x2 + 5x3 1…

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Q: 12. In a standard deck of 52 cards, each card has a suit and a rank. There are four suits (spades…

A: We have to find the probability that the 5 cards in this hand consist of 3 Aces and 2 Queens.

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Q: 1. Verify the initial value theorem for the voltage functions: a. 4+2 cos(t) b. t - cos (3t) and…

A: Given functions are a 4+2costb t-cos3t

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A: Given, Number of sections= 18Number of students= 2000Number of professors= 24To find: Number of…

Q: Find the solution. d³x d?x dx -2-=0 di + di A y =c,e+c y = c+ O y = c,+cc'+ce2

A: Given differential equation is d3xdt3 + d2xdt2 - 2dxdt = 0

Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: We will convert given differential equation into linear differential equation by appropriate…

Q: Let f (x) = e4x. Find p3(2), the value at x = 2 of the third Taylor polynomial about 0, and r3(2),…

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Q: 3. Let F(n) = 9F(n – 1) – 24F(n – 2) + 20F(n – 3) with initial conditions F(0) = 1, F(1) = 5 and…

A: To solve this problem we follow the step below :  Characteristic equation method :  Find…

Q: Question 7 Find the solution. (D² - 2D - 3)y = 0; when x = 0, y = 0, y'= 4 - 3x – e 2x A y = - „3x…

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Q: Solve the given system of linear equations using the LU Decomposition Method. 2.)    x1 - 2x2 + 5x3…

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Q: Which of the following is the general solution to the differential equation (x +2y)dx + (x + 2y +…

A: The given differential equation is…

Q: +00 (x+7)" ITEMS: Consider the power series n=2 2" Vn2 – 1' 1. Use Limit Comparison Test to show…

A: As per the policy we are providing the solutions of first three subparts. Given :  The given series…

Q: 2. Let A = (1,0, 2) and B= (6,-2, 3). Solve for projAB.

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Q: Let c1 (t) = ei + 7 sin(t)j + t*k and c2 (t) = e-Sti + 5 cos(t)j – 7t*k. (Enter your solution as a…

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Q: 1. In at most two sentences, address the following: • Give at least two postulates of Euclidean…

A: Postulate 1 A straight line segment can be drawn joining any two points.Postulate 2 Any straight…

Q: You have $5000 to invest for 1 year.  Fund A has an estimated 4% annual return, and Fund B has an…

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Q: Find the solution. y" - 2y'- 2y = 0

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Q: Determine and draw the graph of the following equation in R3 : z = 1 – e® Also show the traces

A: A quadric surface is a graph in the three dimensional space ℝ3. The trace of a quadric surface is a…

Q: 17. What is the general solution of the differential equation (y² + 9)dx + (3x – 2xry)dy = 0? 2y A)…

A: We have to find the general solution of the differential equation y2+9dx+(3x-2xy)dy=0.

Q: rm of the wayeform

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Q: What is the general solution to the differential equation sin y (x + sin y)dx + 2x² cos y dy = 0 ?

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Q: Solve the system of inear equations, using the Gauss-Jordan eliination method. (Ir there is no…

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Q: You are given: (i) H; 1 for 0 Sx <110. 110-x (ii) 8= 0.05

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Q: a. Write down the 5 nonzero terms of the Taylor series around the point x=0 and find f(2.1) (4…

A: This is a problem of Taylor approximation.

Q: 3. Determination of integrating factors: 2y(x+ y+ 2)dx + (y -x -4x-1y = 0

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Q: What is the particular solution to the differential equation x + (1 + x)y = 12 with y = 0 and 2 - 0…

A: The solution is given as

Q: ) Let A and B be subsets of a universal set U, show that (An B)U (A n B) = A AC B if and only if B C…

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Q: What is the general solution to the differential equation (3 tan x – 2 cos y) sec?x dx + tan x sin y…

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Q: Prove the following using the mathematical induction Let c and d be integers. For every natural…

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Q: Find the solution. (D²-2D-3)y = 0 A y = c,e" +c,e * B y = c,e © y = ce D y =

A: D2+2D-3y=0 Auxillary Equation m2+2m-3=0 ⇒(m+3)(m-1)=0 ⇒m=-3,1

Q: Consider the following IVP: y"+a?y = 0; y(0) = 1, y'(0) = 0 Find the general solution. A) y(t) = sin…

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Q: Let c (t) = ei + 9 sin(t)j + t°k and c2 (t) = e-4'i + 2 cos(t)j – 5t°k. Determine the components of…

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Q: Evaluate the integral shown using Simpson's 1/3 Rule with 20 panels. 12 4arctan dx O 32.52059525 O…

A: Given integral is ∫2124arctanx6dx

Q: (d) If v is an eigenvector for a matrix A and a matrix B then v is an eigenvector for A+ B.

A: TrueJustification:Suppose v is an eigenvector for a matrix A and a matrix B.Then there exist real…

Q: For each of the following relations ~ on sets X, determine whether it is reflexive, symmetric or…

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Q: 5. Given the system 10 2 (a) Find the general solution. (b) Find the solution that satisfies the…

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Q: Write the truth table for P ˅(Q ˅ R) ↔ (Q ˅ (P →(R ˄ R))) ↔(Q ˅ ┐R)

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Q: Find the solution. y-y = -xyl/2 y =(x+2+ce½,? B y = (x+2-ce/½,? © y = (3r - 2+ ce/½,? = (3x –…

A: The given differential equation is ,       y' - y =  - x y(1/2)  Bernoulli equations :  An equation…

Q: What is the interquartile range of the data set below? 3, 5, 6, 6, 7, 8, 9

A: Interquartile range is given by : Q3 - Q1

Q: exercise Find the laplace of each f(t) 2. sin8t sin6t

A: We have to find the Laplace transform of ft=sin8tsin6t

Q: Translate the following sentences into predicate logic : a. All animals like honey b. At least one…

A: Use the given statements.

Q: Ikeoluwa collected data on whether 65 professional golfers have practiced for at least 10,000 hours…

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Q: Se-2t if 0 3,

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Q: QUESTION 1 Given a differential equation (3+x²) + 2.xy= (3 +x² )x² dx (а) Solve the differential…

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Q: Consider and remember that A = (0,4,2) , B = (6,-1,0), C = (3,0,1) 1 1) Determine the unit vector…

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Q: Define f:R → R by ƒ (x) = 5x if x is rational and f (x) = x² + 6 if x is irrational. Prove that f is…

A: Given :  f:ℝ→ℝ  defined by ;         f(x) = 5x,if x is rational.x2+6if x is irrational To prove :…

Q: O A. Point (0,a) is in the domain where a E R; O B. The sketch of the domain of f is only def ined…

A: This is the problem of function.