Q.1 Given the following data 0.050 13.00 0.074 14.60 0.089 15.00 0.10 16.20 0.14 18.23 0.16 20.11 fi evaluate a fitting polynomial using the least squares method in two ways. The first using the usual polynomial in powers of x up to first order, and the second using the orthogonal polynomials uk (x).

Q: rel= = 0A 15, x² = 4(4x² - 1) If, 2 Prove that, x = √√5 +√√3

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Q: 1. Let S be the portion of the surface x² +22= 1 lying in the first octant and bounded by x = 0, y =…

A: x2+y2=1 and x=0,y=0,z=0 and y=4-2x.

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A: If you observe the contour map is hyperbolic so the graph f should also hyperbolic

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A: Suppose T:R2→R2 is given by T(x)=-1-5-34X      (1) To find the matrix M of the inverse linear…

Q: Exercise 4. For a multiplicative function f, define the Dirichlet series for f by L(s, f) = f(n) We…

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Q: Find the general solution for the following differential equation y(3) +y'-10y=0

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Q: Use calculus to find the exact Cartesian coordinates of the leftmost point on the parametric curve x…

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Q: Evaluate the given integral by changing to polar coordinates. 16 e-x² 。 -x² - y² dA' where D is the…

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Q: Use the Taylor polynomial around 0 of degree 3 of the function f (x) = sin x to find an…

A: Here the function is given by fx=sinx, using the Taylor polynomial around 0 of degree 3 of the…

Q: 4. Find the image of the region {(x,y): 0≤x≤2,0 ≤ y ≤ under the transformation w=e². Draw the image.…

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Q: A rabbit population rises and falls each year. It is at a minimum of 5000 rabbits in January and a…

A: A rabbit population rises and falls each year. It is at minimum of 5000 rabbits in January and a…

Q: Find the inverse of the matrix (if it exists). (Round your answers to four decimal places. If an…

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Q: Only set up the triple iterated integral in the given terms, do not solve for volume.

A: We have set up the integral dydxdz and find the volume

Q: */ // * Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (4,0,0), (0,6,0), and…

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Q: : Find Fourie trans form? alt) = 5 rect(134) @ F[ 21-2) 120+ ]

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Q: This is incorrect

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Q: Use an inverse matrix to solve each system of linear equations. (a) x + 2y = 1 x - 2y = -3 (x, y) =…

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Q: Let *=(-2+2·2+2) be the vortex field. Determine / F. dr for each of the paths. (D) (Use symbolic…

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Q: 0 00 6 GTA If, x² = 4 (4x² - 1) Prove that x = √√5 + √√3

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Q: Let fn(x) = 1+cos2 2023 (na). Does {f} converge uniformly to a function f on R? √n

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Q: Give an example of a set that satisfies the condition, or prove that one does not exist: An…

A: The statement or condition :An infinite intersection of non-empty closed sets that is empty.

Q: 9.22. Let F be a field, let f(x) = F[x] be a separable polynomial of degree n ≥ 1, and let K/F be a…

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Q: Show that the matrix sin [. A-¹ = A = -cos is invertible and find its inverse. cos 0 sin 8

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Q: (1) Is Mmxn(R) a vector space over the rational numbers Q? Explain. (2) Is Mmxn(Q) is a vector space…

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Q: Which Riemann sum represents the illustration shown? 3 L 2 1 2 4 6 4 O 8 10 √xi. Axi √æi. Axi xi.…

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Q: B3.3.4.1f) (1) Use limit laws and SL. 1 - SL. 8 for sequences, to evaluate the following limits: cos…

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Q: Find the equation of the cubic that best fits the given points: (-3, 1), (0, -1), (2, 5), (4, 2),…

A: X Y -3 1 0 -1 2 5 4 2 5 0

Q: 2. Consider the following functions: • f1(x) = sin(7₁) cos(12); • f2(xy) = x¹y; • fs(x)=xx¹; • f4(x)…

A: Consider the following functions: f1x=sinx1cosx2 f2xy=xTy f3x=xxT f4x=Ax To Find: a) Dimension of…

Q: find the Laplace transforms of the following functions: (a) f(t) = (sinh 4t)(sin 5t) (b) g(t) =…

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Q: Let D = {z € C|1 ≤ 2 ≤ 2, 0≤ Arg(2) ≤ R}, f: C→C with f(2)=1/2². Find f(D), then sketch the picture…

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Q: Recast the equation y""- cos (y +t)y" + e" y = 0 as a first-order system of ordinary differential…

A: Equation : y''''-cosy+ty"+ey'y=0

Q: 3. (a) Show that an eigenvector cannot be associated with two distinct eigenvalues. (b) Let A be…

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Q: Find the solution of the following system if (0) = -9 and y(0) = 7. x' (t) = x(t) - 4y(t) y(t) =…

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Q: 6. Find the Maclaurin series for g(x) S™ g(t) dt. = cos x - 1 + −1+1/2/22 x² and h(r) =

A: The above series is the Maclaurins series for g(x).

Q: (1) Use these (₁) (2) (us . 1 1 D and () 1 1 J Draw by ( (b) (vi) 0 1 I 1 0 1 1 I the (i) ↑ 1 1 1…

A: Given matrices

Q: Evaluate the triple integral Enter an exact answer. Provide your answer below: z=1 y=zx=-2y-2z+2 Ĵ Ĵ…

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Q: Calculate the root of f(x) = 2x + 3 cos x + e^-0.1x in the interval [-2,-1] with the Newton-Raphson…

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Q: Find the image of {z = x+iy € C: -1 ≤ x ≤ 2, n<y< 2π} under the transformation w = e².

A: z=x+iy∈ℂ:-1≤x≤2,π&lt;y&lt;2π

Q: and COMI jc janod adject STROSEd HD mol Kane jo sangen and jeung and danig

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Q: (1) Derive a system of differential equation to represent the rate of change of the exchange rate…

A: We begin with the asset market to generate a set of differential equations for the Dornbusch model:…

Q: An object occupies the volume of the upper hemisphere of x² + y² +2²=4 and has density z at (x, y,…

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Q: value of the detminant at the given critical point find the value of fxx at the given critical…

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Q: 2. Prove that ƒ : (R × R, +) → (R, +) given by f(x, y) = x + y is a homomorphism. Is g : (R × R, +)…

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Q: Use (a) parametrization; field (b) Stokes' Theorem to compute fF. dr for the vector F = (x²+z)i +…

A: Given:F=(x2+z)i+(y2+2x)j+(z2-y)kC: intersection of x2+y2+z2=1 and z= x2+y2

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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