Let  z = f(x,y) = x2 + xy Find the linearization of f(x,y) when x = 1, y = 3 Find the equation of the tangent plane to the graph of f(x,y) when x = 1, y = 3 Find the differential of f(x,y) Find the differential of f(x,y) when x = 1, y = 3

Q: Find the general solution of the given second-order differential equation. 3y" + 2y' + y = 0 y(x) =

A: 3y" + 2y' + y = 0

Q: Solve the given differential equation by undetermined coefficients. y" + 4y' + 3y = 6 y(x) = =

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Q: use the successive approximations method to Solve the following Volterra integral equations: 1-/22²…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: If n = 12 m (me N), prove that "C₂ (2+√3)² "Co- - + "C4 (2+√√3)4 n "C6 (2+√3)6 ·+···=(-

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Q: (iii) =Tb-kt dn ds

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Q: Find vectors x and y with ||x, = 1 and ym 1 such that ||A||₁||Ax|, and A||- ||Aym' where A is the…

A: Given, The matrix  A=4-1-230-3102 We have to find the vectors x and y with xs = 1  and ym = 1 such…

Q: 5) Show that the equation xy" + y = 0, x > 0, has a regular singular point at x = = 0. Determine the…

A: The given differential equation is xy"+y=0 with x>0. The given differential equation can be…

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A: Given: Two sprinklers with a spray radius of 50 feet are located 50 feet apart. To find: Total area…

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Q: 2. A linear system is described by the following equations. = -3 2a 2b + c a +36-2c = 1 3a-b-c = 2…

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Q: η Σ() = 2 – n+2 2n

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Q: 10. A professional athlete invested $2.5 million of a bonus in an account that earns 6.8% compounded…

A: To find semi annual years when the account will be $0 We use ordinary annuity formula

Q: Suppose that three geological study areas are set up on a map at points (-13, -11), B(-9, -12), and…

A: The study center is located at A-13,-11, B-9,-12 and C-4,-10. The scientist estimated the epicenter…

Q: 8. If $88,000 is invested in an annuity that earns 5.8% compounded quarterly, what payments will it…

A: The formula for amount invested in an annuity is given by: An=R1-(1+r)-nr where  An=Amount invested…

Q: A shelf in the Metro Department Store contains 100 colored ink cartridges for a popular ink-jet…

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Q: f is a function with the following Fourier coefficients on the interval [-, π] ao= - a₁ = b₁ === a₂=…

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Q: F. Answer the following. 1) Without solving for the actual roots, find the sum and product of the…

A: 1) We know for a quadratic equation            ax2 + bx + c = 0 [a, b, c are scalars, a ≠ 0]     Sum…

Q: Prove that 3! 26η 13) = Σ (1) r+3 C

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Q: Let P(Z) = 0.40, P(Y) = 0.43, and P(ZnY) = 0.19. Use a Venn diagram to find (a) P(Z'NY'), (b) P…

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Q: Prove that for all integers n ≥ 1, 10" = (-1)" (mod 11). Use part (a) to prove that a positive…

A: (a) Let n≥1 be an arbitrary integer. We know that 10≡10mod 11≡-1mod 11. Now consider 10n:…

Q: Problem 6. Use the Gram-Schmidt process to find an orthonormal basis for the column space of the…

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Q: Give an example of a real function that is increasing on the interval (0,2), and decreasing on (2,…

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Q: 6. As discussed in class, functions have different power series because their coefficients differ.…

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Q: 1. Consider A function f(x) = x³ - 7x² + 4x + 12. (a) (b) (c) (d) (e) Construct two different fixed…

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Q: Find a potential field for F(x, y, z) = (y +z)i + (x + z²)j + (x+2yz)k or prove none exists.

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Q: Let ABC be a triangle, and DE parallel to the base BC. Suppose point F is any point on DE. Show that…

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Q: Separation of Variables Sote the separable equation: cosx cosy du se 2=-=-=-* du sin(x) y

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Q: There are 79 people protesting the destruction of the rain forests. There are 31 ​males, 24 of whom…

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Q: A pair of dice is rolled. Find the probability of rolling a) a sum not more than 8, b) a sum not…

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Q: 12.1. For each of the following domains, determine whether it is simply connected, multiply…

A: A domain D in C is simply connected if it's complement with respect to Cinf is a connected subset of…

Q: (b) Compute the flux of the vector field F(x, y, z) = yi + zk upwards through portion of the cone z…

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Q: Question: 7. A small country consists of 7 provinces with the populations according to the table…

A: Given: Province Population A 25312 B 19734 C 33407 D 29591 E 13288 F 22751 G 31992…

Q: Graph the region R bounded by the graphs of the indicated equations. Describe R in set notation with…

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Q: {0.0 (a) Find an orthogonal basis of W. Show your work. (b) Let v = [1 2 3 4]. Compute projw (v).…

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Q: 0.1 Soe O exida x³dx Series rep A ex = 2 8/3 n!

A: The given problem is to evaluate the integral of ex^3 from 0 to 0.1 by using the first 5 terms of…

Q: Consider the initial value problem +16y=48t, y(0)=9, (0) = 5. a. Take the Laplace transform of both…

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Q: Sketch the curve with polar equation r = cos(30), 0 ≤ 0 < 2π, plotting only the points with r≥ 0 and…

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Q: A vector field is said to be incompressible if its divergence is O. Show that any vector field of…

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Q: 1. The product of the ages, in years, of three teenagers is 4590. None of the teens are the same…

A: ANSWER 1: Let the age of three teenagers be x, y, z respectively Given that the product of their…

Q: 3u² Suppose w(x, y) = (x²y+e), where y=vsin(uv) and x=ln √2v value of method. dw dw ди ду when π √2…

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Q: Suppose f(x) = x + 3x + 1. In this problem, we will show that f has exactly one root (or zero) in…

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Q: . Let a, b € Z so that 4a + 5b is a multiple of 13. Prove that 13 divides 9a + 8b.

A: We have to show that 13 divides 9a+8b To prove this we using 4a+5b divisible by 13

Q: Determine the following system, x1 + x2 - x3 + 2x4+x5 = 0 x1 + 2x2x3 + x4 + x5 = 0 2x1 + 3x2 - x3 +…

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Q: is that The necessary and sufficient condition that a curve is a plane curv N T T

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Q: Consider w = F(x,y,z) = x2 + yz3 Find the equation of the tangent when x= 3, y = 2, z = 1.  At…

A: The given surface is Fx,y,z=x2+yz3. (1) The given point is x=3,y=2, z=1. We know that the equation…

Q: 6. If A is an invertible matrix, show that its projection matrix, P, is the identity matrix, I.

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Q: 5. Evaluate the integral F.dS where F = (2x, y, z) and S is the boundary of the solid cylinder x² +…

A: Given  F→= 2x,y,z       equation of boundary of the cylinder is x2+y2=1…

Q: Remark: For positive integers n, m, we have • (n) n (m) (n) + (m) = = (lcm (n, m)) (gcd (n, m))

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Q: Suppose a triangle has the following vertices: v1 = (-2, 3, 6) v2 = (4, 5, -1) v3 = (3, 3, 0) What…

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Q: 2- Find the connected components of this graph and illustrate your method. H

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