Let F : R" → R™ and g : R" → R. Prove that d(gF)[a; h] = g(a)dF[a; h] + F(a)dg[a; h].

Q: dy For = 2x -9 and y(0) = 7, use Euler's method with h = 0.1 to approximate y(0.4). Then, solve the ...

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Q: For spring-mass model x" + ' + x = cos(wt), find the practical resonance frequency, and the steady p...

A: For the spring mass model  mx''+bx'+kx=Fcosωtsteady periodic amplitude is given byCω=Fk-mω22+bω2prac...

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Q: Which of the following is the factored form of x^3 + 3x^2 – 10x – 24? * - O (x - 4)(x – 3)(x – 2) O ...

A: Let f(x) = x3 + 3x2 - 10x - 24

Q: a) How many edges does a K20 graph have? Answer: b) What is the degree of each vertex of a K20 graph...

A: Since  you have posted a multi subparts question according to guildlines I will solve first  three q...

Q: Find y as a function of a if y" – 8y" + 15y/ = 8e", y(0) = 28, y(0) = 14, y"(0) = 12. y(x) = 52.04-(...

A: We have to find the solution of differential equation.

Q: Let f: ZxZ → Z×Z be defined by the formula f(x, y) = (2x+3y, x+2y). (1) Find the inverse map g = f ^...

A: Since f is a linear transformation and f is a linear operator. So if f is one to one then imply f is...

Q: 6. Let a be a real number. Consider the series Σ cos(n7) An, where An = 2n + 1 n=0 (a) Is it possibl...

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Q: What is the remainder when (5x^100 + 5) is divided by (x – 1)? * - 10 5 10 - 5 Factor: x^3-12x^2+47x...

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Q: Consider the vector v between (-5, 5, –3) and (1, 1, 1).

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Q: The temperature T (in degree centigrade, °C) in a solid metal sphere is given by the function e-(2+y...

A: Given T(x,y,z)= e-(x2+y2+z2)1)The rate of change of temperature in the direction of X-axis is ∂T∂X∂T...

Q: Solve dx- dy

A: Here we can use variable separable method to solve the given differential equation. This method is a...

Q: 5. Determine the values of m and n for f(x)=mx³+20x²+ nx- 35 given that (x+ 1) gives a remainder of ...

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Q: 2. Pinocchio's nose length y (in inches) is dependent on his lie count s. Geppetto has modeled this ...

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Q: * e りこ0 ピッ そ= -> ズ

A: Introduction: The second order non-linear differential equation of the form  x2y"+xy'+x2-n2y=0 is re...

Q: b Write the vector b in terms of the other vectors. C.

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Q: Let a = and b =. Show that there are scalars s and t so that sa + tb =. You might want to sketch the...

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Q: 2. Pinocchio's nose length y (in inches) is dependent on his lie count s. Geppetto has modeled this ...

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Q: Find the linear approximation to R(t) = fifth root of t At 1=32. Use the linear approximation to app...

A: Introduction: For a continuous and differentiable function fx, its linear approximation is formulate...

Q: 2. Recall that the characteristic function of a set E is defined as I is in E 1, Xe(z) = { 0, z is n...

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Q: if x 4.

A: The function gx is a piecewise defined function.

Q: 1. Let f(x) = { a sin ! r +0 i r= 0 i Is f(x) continuous at 0? Justify ii If f is discontinuous at 0...

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Q: Let f(x) be defined as f (x) = e* + 2x2 %3D a) Starting with the initial interval [-2,2], perform th...

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Q: A. A Find the value of the indicated variables. S 13 у -5 2 1. 22 26 4 1 5. 3. y +3 6 14 15 45 2. 16...

A: Solve the equations

Q: E. Solve the following equation algebraically. Explain your process. [A

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Q: Jan deposited an amount of money in the bank. If interest rate of the bank decreases from 4 3/43% to...

A: The rate of interests can be simplified as follows: 4343%=17543%,412%=92%

Q: Task 1. Using the Eigenvalue method, solve the system x' Ax for -1 0 0 0 2 A = Show that some (nonze...

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Q: 10. Given: f(x, y) = -x² – y² + 4. a) Draw an accurate graph of the portion of f(x, y) that is above...

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Q: 3) f(t)= (t+1) sin (t+2)= +sinltt2) + sint +2) Asin(2)+ 1- Colは) ds s Sin(2) +1- COnd ペ+ ( ニ +1) - s...

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Q: If a cup of coffee has temperature 93°C in a room where the ambient air temperature is 23°C, then, a...

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Q: Use the definition of the functional limit to prove the following: (a) lim 4x + 3 = -5. x→-2 (b) lim...

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Q: f(x)=6x-10 , g(x)= x^2+3x+8 (gof)(-2) = %3D 55 none of these 25

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Q: • Problem 4: Let (M,d) be a metric space and let A C M be non-empty. Prove that the following are eq...

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Q: Solve the L.P.P using Simplex method Max Z= 3x 1 + 2x 2 + 2x 3 Subject to 5x 1 + 7x 2 + 4x 3 ≤ 7, 4x...

A: The given problem is to solve the linear programming problem using simplex method.

Q: A cube is located such that its bottom four corners have the coordinates (-4, –5, –1), (-4, –1, –1),...

A: Solution:-

Q: b) The point (-9, -2446) is on the transformed function f(x)=7|}(x, 5)|3– 45 use the transformation ...

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Q: dy 12. (1 + x) dx xy = x + x²

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Q: 5.13 A square matrix is a matrix that has an equal number of rows and columns. In mathematics, m x m...

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Q: What is the angle in radians between the vectors а %3 (6, 8, -2) аnd b = (-7, 7, 0)? Angle: (radians...

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Q: Suppose you are taking a bus trip from your home in Florida to California. There are seven different...

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Q: 14. xy' + (1 + x)y = e¯*sin2x %3D

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Q: f(2) = { a sin ! r+0 i r= 0 1. Let i Is f(r) continuous at 0? Justify ii If f is discontinuous at 0,...

A: We have to check the given function is continuous at x=0.

Q: A thick spherical shell occupies the region between two spheres of radii a and 2a, both centred on t...

A: The complete solution is in below

Q: 13) Expand fit) in Fourier series in the interve) (-2, 2) when fit) = -zst <o

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Q: In answering a question on a multiple-choice test, a student either knows the answer or guesses. Let...

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Q: Convolution method: Find the function whose Fourier transform is 1 (4 + k2)(9 + k²)

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Q: 11) Find the moment of inertia and the radius of gyration of the solid formed by revolving 1 the reg...

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Q: ive of f(x, y, z) 1) in the dired

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Q: aces x2 + y2 pint (2, -1, 2)

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Q: (Hand-gwsutten solution only) D Convert the fellowing egn into three Ist ander diffentahel y" - 3 y'...

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not men...