Give a proof of the chain rule arguing separately in the case when every neighborhood of zero contains a value of h for which Ahf(x) = 0.

Q: subspace spanned by = X₁Y₁X₁Y2X2V₁ + 4X2Y2, and let P be the orthogonal projection of R² onto W.…

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Q: Find the quadratic y ax²+bx+c that best fits the data points (-2,-43), (-1, 79), (0, −55), (1, −5),…

A: We have to find the quadratic y = ax2 + bx + c that best fits the data points (-2,-43), (-1,79),…

Q: ng the Euclidean Algorithm, what is the monic gcd of f=x^4+3x^2+2x+4 and g=x^2-1 in ℤ_5[x]?   1 x-1…

A: We can use the Euclidean algorithm to find the gcd of f and g in ℤ_5[x]

Q: Write it properly please I cannot read it well especially no 2

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Q: Use the Lagrange multiplier method to solve Max U = xyz² subject to X-y + z = 20 Verify that the…

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Q: 2 1 X 1 2 1 1 23 = 0

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Q: A particular manufacturing design requires a shaft with a diameter of 19.000 mm, but shafts with…

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Q: Suppose that the price S(t) of a share follows the GBM with parameters S, μ, o, r. Consider an…

A: Introduction: In probability theory, a probability distribution is a mathematical function that…

Q: e 10. For each situation, write a scalar equation of the plane. (7, 9, -1) and a) has normal n…

A: We have to find the equation of plane.

Q: Find a square root of the matrix 1 A 1 = (₁ -5 2 ₁ ¹ + ²i). 9

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Q: © L +/ N

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Q: Consider the function f(x) = 3x + sin x - e* the graph of which appears on the left. Approximate the…

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Q: How O Lt 9/2

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Q: Suppose that we use the Improved Euler's method to approximate the solution to the differential…

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Q: The group (U20, X20) = {(1, 3, 7, 9, 11, 13, 17, 19), ×20} has subgroups H = {1,3,7,9) and K =…

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Q: Consider the following all-integer linear program. 1x₁ + 1x₂ 4x + 6x₂ s 34 1x + 7x₂ X₂ 2x₁ + 1x₂ =…

A: Answer : 4th graph is correct .

Q: Find a basis for Q(√2, √6 + √10) over Q(√3+ √5).

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Q: Suppose that R is the finite region bounded by f(x)=√x and g(x) = 2 2. Find the exact value of the…

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Q: 13) Find and graph all the roots in the complex plane for V-8 + 8i

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Q: Let U={10,20,30,40,50,60,70,80.90,100}, A={20,40,60}, B={40,80,90,100}, and C={30,60,70,90}. Find…

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Q: 2 J4y-yz dy | 1

A: We have to find the total shaded area .. So the yellow shaded portion in ist and 2nd quadrant.. So…

Q: Evaluate the integral given below. √ (2x - y²) dx + xy dy Where C is given by: x = 8t, y = √t. 0 ≤ t…

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Q: Learning Target DA4: I can find the critical values of a function, determine where the function is…

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Q: 2) Use logical equivalences to show that (P^q) =-pv-q.

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Q: 4. Find the Maclaurin series of the following function and use it to evaluate f(n) (0) f(x) =…

A: The given problem is to find the maclaurin series for the given function and use it to find the…

Q: 6. Let B be the matrix given below. B = (b) X = [4 5 5 0 4 0 0 -5 (a) λ = 4 is an eigenvalue of B.…

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Q: What is the degree of ℚ(u,v) over ℚ(u) if u is the square root of 2 and v is the square root of 8?…

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Q: What is the degree of the splitting field of f=x^4-2 over ℚ?   4 6 8 None of the above

A: The degree of f(x)=x4−2 is 4, so the splitting field K of f(x) must contain its 4 roots. Let α=24…

Q: What is a solution to the equation x^2+x+4=0 over ℤ_6?

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Q: Let V be an inner product space. Suppose that TEL(V). For u, v € V define (u, v)T by (u, v)T = (Tu,…

A: Introduction: An invertible positive operator is a linear operator on a vector space that is both…

Q: Use determinants to find out if the matrix is invertible. 5 0 -1 2 -6 -4 0 10 6 The determinant of…

A: Let the given matrix is ,                A =   5    0 -12 -6 -40   10    6 (.)  An square matrix is…

Q: Find the linear approximation of the function f(x, y, z) = √√√x² + y² + z² at (6, 9, 2) and use it…

A: The given function is f(x,y,z)=x2+y2+z2. To Find: A linear approximation of this function at…

Q: In this problem, y = c₁ex + c₂ex is a two-parameter family of solutions of the second-order DE y" -…

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Q: y = AX y = 1 1.5 y = 2 2.5 3 y 35| 66 55 65 Paste the table into Desmos and fit the requested type…

A: Given data is: x y 1 35 1.5 46 2 55 2.5 65 3 74 Paste the values from Excel in…

Q: The quantity, Q, of a certain product manufactured depends on the quantity of labor, L, and of…

A: Answer

Q: The signal x() exp(-at)u(t) is passed as the input to a system with impulse response…

A: We have given a signal ..with the help of the Fourier transform we find energy ..the procedure is…

Q: 5. Prove the following statement if it is true. Otherwise, provide a counterexample. a. Let x, y E…

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Q: Find the flow vector 7(x, y) and sketch the flow field for the differential equation dy/dx = x+y.

A: Given:  The differential equation: dydx=x+y To do:  Find flow vector v→(x,y). Sketch the flow field…

Q: Consider the initial value problem y"-y-6y= 0, y(0) = α, y'(0) = 5 Find the value of a so that the…

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Q: 1 What is the product when f(x) = 3x² + 2x - 4 is multiplied by g(x) = 4x² + 2 in Z5 [x]? Enter your…

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Q: Quadratic polynomial factors should be typed as (x^2+ax+b)(x^2+cx+d) L Factor f(x)=x-2x²-x-2x-2 €…

A: Using Ferrari's method to split the biquadratic polynomial.

Q: Let F=w XR, where is a constant. Compute f F dR along the straight line from (0,0,0) to (2,2,2).…

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Q: Solve the given differential equation by separation of variables. dy = (2x+7)³² dx 8x 9

A: The given differential equation is         dy/dx = ((2y+7)/(8x+9))2                     =…

Q: In R4 let M be the subspace spanned by the vectors (1, 1, 1, 0) and (0, -4, 1, 5) and let N be the…

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Q: Find the absolute maxima and minima of the function on the given domain. 13) f(x, y) = x2 - 2x - 2y2…

A: The given function is fx,y=x2-2x-2y2+2y . And the given region is the triangular region bounded by…

Q: Find the eigenvalue and eigenspace for the given matrix 4 2 3 -1 1 -3 2 4 9

A: The given problem is to find the eigen values and eigen spaces for the given matrix. We have to find…

Q: Q22 Calculate the directional derivative of the function f(x, y, z) = xy cos(8yz) at point (2, 3, 0)…

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Q: Circumference (mm) 150 135. 120. 105. 90. 75. 60 45 30 15. y 16 Radius (mm) | X

A: We need to find the domain and range of the function from the graph:

Q: he polynomial f= x^3- 4x + 2 is irreducible over Q. Let u be a root of f in some extension Q(u) of…

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Q: Use the information provided to write the general conic form equation of each hyperbola. 8)…

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