QUESTION 2 If y-sin-¹ z, show that d'y Hence, deduce that -(1)-(2) - <- 0. dz = M dz dz

Q: Find and classify the critical points of the function f(x, y) = 4x²y - 2x - y².

A: We need to determine and classify the critical points of the function: f(x, y)=4x2y-2x-y2.

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A: This is a question of linear transformation.

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Q: 8. (2, x=0 : Let f R2R be given by f(x, y)=3, x=2 (7. x (0,2) that f is integrable on R. and R=…

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Q: 28 Use the Integral Test to determine if the series shown below converges or diverges. Be sure to…

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A: Given information Velocity v=x't and acceleration a=v't =x''t Given table is

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Q: Sketch the vector field F(x, y) = (−x — y, x - y) at the points (x, y) where x, y = {-1,0, 1}.

A: given vector field F→x, y=-x-y, x-y we have to sketch for x, y∈-1, 0, 1

Q: True or false? For all sets A and B,  (A∪B)'=A'∪B' This can be determined by constructing a…

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Q: (b) Find the fundamental matrix Þ(t) for the system x' = Ax which satisfies (0) = I. (c) Use Þ(t) to…

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Q: By using logical equivalences and de Morgan's rules, we can show that the statements p v q and (p…

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Q: (5) Let f: RR be twice-differentiable f(x) ≤0 and Prove that f is constant on R. on R. Suppose that…

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Q: Pure water has a pH value of 7.0. How many times more acidic is milk, with a pH value of 6.4, than…

A: Given that:      pH value of Pure water = 7.0      pH value of Milk            = 6.4

Q: Determine the Fourier transform of the following: f(t) = {e¹³t 0, −1<t<1 elsewhere

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Q: City high school had a student reduction and lost 1/10 of its students. if 198 of its students were…

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Q: Use Sigma or Pi symbol to condense the following expression: 3 X X ΟΠΩΣ Π 5 16 22 i=3 (i-1)² ΟΣΤ τ X…

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Q: This is NOT a possible solution of a first order system of homogeneous equations with constant…

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Q: Q-3: a) Let R be a relation on A = {1,2,3,4} such that aRb means |ab| ≤ 1. Find the matrix…

A: (a) It is given that, R be a relation on A = {1, 2, 3, 4} such that aRb ⇔ a-b≤1 We have to find the…

Q: Consider the nonhomogeneous differential equation: -2y+ y = - (E). Given that 3=e" and y₁=xe are two…

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Q: This problem is an example of critically damped harmonic motion. A mass m = 6 kg is attached to both…

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Q: - Show that (a + b)" = a + bn mod 2 for all integers a, b, and n with n > 0. Hint: Try looking at…

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Q: EX LeT X= {1,2,3,4} find The Possible Topology That Contain ses [1,2], [2,3],[1,3,4} .

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Q: 3. Solve each of the following congruences. (a) 6x + 3 = 4 mod 10 (b) 6x + 3 = 1 mod 10 (c) x² = 1…

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Q: Wind speed (km/h) V t 5 20 0.6 30 80 1.2 40 1.5 60 2.8 10 0.6 1.3 2 2.2 Duration (hours) 15 20 0.6…

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Q: 1Q: Using Newton's Method solve the following system of equations by taking the initial guess as x =…

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Q: Let x²y" + 4xy' - 4y = 0 be an ordinary differential equation. Knowing that y, (x) = x is a solution…

A: we use the standard formula to solve this problems .

Q: At time 0, Cheryl deposits X into a bank account that credits interest at an annual effective rate…

A: Solution:

Q: Use an appropriate test to determine whether the series given below converges or diverges. Σ n=1 5n+…

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Q: Let A = {x € R]−1≤ x ≤ 4}, B = {x € R| 4 ≤ x ≤ 6}, and C = {x € R|3 ≤ x 6}

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Q: Define the relation R on the set of integers as Vm, n EZ, m Rniff 5|m - n Determine if the relation…

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Q: Express Ln(z) in the form a + ib. (Simplify your answer completely.) Saman In(2)+1(-)

A: Given a complex number z=4-4i To express lnz in complex form.

Q: The general solution of the second-order differential equation y"-y-12y = 0 is: y = c₂e³x + c₂e-4x…

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Q: Use the following property of the definite integral to estimate the definite integral: f/4 π/6 […

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Q: Determine the values of α, if any, for which all solutions of the differential equation y" (2a 13)y'…

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Q: b)Estimate the value of cos 0, at 0 = 5°with the help of the following table 0⁰ 10⁰ 20⁰ 30⁰ 40⁰ 50⁰…

A: The given table is: θ 0 10 20 30 40 50 sinθ 0 0.1736 0.342 0.5 0.6428 0.766 We have to…

Q: Evaluate: 3/20° × 15/45°

A: the given expression is 3∠20°15∠45° Multiply the polar magnitudes and add the angles of the complex…

Q: Determine a shortest parameter interval on which a complete graph of the polar equation can be…

A: To Determine:  The shortest parameter interval on which a complete graph of the polar equation…

Q: Show that the vector field 1 F(x, y, z) = (- :)= (-2: 25³ sinh (2y − 1) - x²y is conservative by…

A: If a vector field F→(x, y, z) is conservative then there exists a potential function f(x, y, z) such…

Q: Q: Prove the following transform; formula's by t a) L [ F+g] = { [ [ 56(0)3(²-1) 47] = F (S) G(S) b)…

A: Given :             a Lf*g =L∫0tfu gx-udu =FSGSbLtnft=-1ndndsnFSc Lδt-t0 =e-st0 To prove : prove…

Q: Q4. Let R be the annular region lying between the two circles x² + y² = 1 and D x² + y² = 16.…

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Q: Let yty + 0.1y³ and y(0) = 1.1. Use Euler's method to find approximate values of the solution of the…

A: Given: Euler's Method: For a given IVP y'=f(x,y), y(x0)=y0 the iteration is given by yn+1…

Q: 1. Find and classify the critical points of the function f(x, y) = 4x²y - 2x - y².

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Q: 1. Evaluate the following integral S² a. Analytically b. Numerically using: -20 20x7 + 5x5 + 15x³ +…

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Q: Use the method of variation of parameters to find a particular solution of the differential equation…

A: Use the method of variation of parameters to find a particular solution of the differential equation…

Q: 2. Find the eigenvalues and eigenfunctions of the given boundary value problem. y" + xy = 0; y(0) =…

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Q: Problem 2. Find interval of the solution where the initial value problems below is defined. (a) ty"…

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Q: Q1. Show that the first four Laguerre polynomials [named for the French mathematician Edmond…

A: Result: If dimension of a vector space V is n then any linearly independent set containing exactly n…

Q: . Define points P = (-3,2,0), Q = (0, -4,3) and R=(2, -7,2). (a) Find the vector equation,…

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Q: 1. Express the given functional equation in terms of: a. Graphical b. Tabular form c. Sequence x(n)…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…