1. I. TAYLOR SERIES - Find the approximate value of sin (0.1) using Taylor Series of 0(h³).

Q: If the set W is a vector space, find a set S of vectors that spans it. Otherwise, state that W is…

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Q: Is f(x) = (x sin(x)) / (1+sqrt(x)) uniformly continuous on [0, infinity) ?

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Q: 13. Verify that F(x, y) = (exy + y)i + (ex+x) j is conservative. Find a potential function for F.

A: Given: Fx, y=exy+yi+ex+xj (a) To verify F is conservative. (b) To find potential function for F.

Q: For each function below, find all points where the function is discontinuous and classify the type…

A: To Check: whether the following function are continuous or not. If they are discontinuous we need to…

Q: d) x1 + 2x2 + 2x3 + 5x4 = 11 2x1 + 4х2 + 2x3 + 8x4 = 14 x1 + 3x2 + 4х3 + 8x4 = 19 X1 - X2 + X3 = 2

A: We solve the system of equations.

Q: Find the Laplace transform of f(t) = e-2t + 2 sin2t

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Q: 4. Find the surface area of the part of the sphere x² + y² + z² = 1 above the plane z = 1/√2.

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Q: 5. Let ƒ(x,y,z)=2xy²z² − 3xy a) Find the rate of change of ƒ (x, y,z) at P(1, 1, -2) in the…

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Q: Consider the differential equation defined by the auxiliary equation (D² - 1)y = 0. Find the…

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Q: Nutrition Use duality to answer the following application. Or makes on food out of giraffe end…

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Q: Explain the diagonal-proof method Question 1. Name and explain the proof method that is used to show…

A: We need to explain the proof method that is used to show the uncountability of sets, incompleteness…

Q: 7. You are constructing a 480 cubic feet box. The bottom of the container costs $5 per square foot…

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Q: Question 2 a) Evaluate £{est}. b) Evaluate L{(t− 3)² + sin 7t + cos 8t} c) Use the Laplace transform…

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Q: Question Using the Method for Variation of Parameters, u₁ is evaluated by the following expression:…

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Q: If we use the Method for Variation of Parameters to solve a nonhomogeneous differential equation for…

A: To solve non homogeneous differential equation,  we use method of variation of parameters.

Q: that follow. 13. Suppose a radioactive element decays in such a way that for every hour that passes,…

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Q: 8. A company wants to assign 8 salespeople to 4 regions of a state (see table below). Region…

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Q: Does there exist false although its contrapositive Justify your answer. statement that is is true? a

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Q: Let A = -2 10 2. One of the eigenvalues of A is X = 2. 020 -1 4 1 a) Find a basis for the eigenspace…

A: Given: A=-2102020-141, λ1=2 To find (a) Basis for the eigenspace of A associated with λ=2. (b) Other…

Q: 7. Given f(x) = - 2log (6 - 2x) + 3 a) Determine the following information; show your calculations.…

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Q: Let R = ({0, 1, ..., 8}, , 0, 0) Ⓒ) be a ring where a a and are defined as follows: b = (a + b) mod…

A: a) zero element is 0 b) unit element is 1 c) a non zero element is said to be zero divisor , if…

Q: 8. Evaluate the line integral [x²dx + xe¯dy where C is the closed path along the triangle in the…

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Q: Please answer the question. Asap. Thank you.

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Q: Write the given differential equation in the form L(y) = g(x), where L is a linear differential…

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Q: Find the standard matrix of the linear transformation T. T: R² -> R² rotates points (about the…

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Q: 3. (a) Let f: X → Y and g: Y→ Z be functions. Prove the following statements. If f and g are both…

A: We can prove the following parts .

Q: Determine whether the set of solution defined by {ex, e2x, e-x} is linearly dependent or linearly…

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Q: Determine whether the set of solution defined by {ex, x², 3x} is linearly dependent or linearly…

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Q: Find an equation of the plane that passes through the points (4, 2, 1) and (4, 1, -5) and is…

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Q: 2. The state sales tax in Kansas is 6.5%. If the state tax on a purchased item is $2.38, what is…

A: Answer for this question is $39. The solution is below in the step 2 part.

Q: Find the volume of the solid bounded below by the circular paraboloid z = x² + y² and above by the…

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Q: p) Find the volume of the solid obtained by rotating the region bounded by the cures y = ex/², y =…

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Q: Jo z(2x + 2y)¹/2² ln(2x + 2y)ds C

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Q: 2 W S F2 Determine whether the system is consistent. 5x1 + 2x2 + x3 = -11 2x13x2x3 = 17 7x1 + x2 +…

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Q: Which of the following differential equation is associated to a solution definec y = 2cosh2x -…

A: We can find differential equations.

Q: Determine the flux of F(x, y, z) = across the surface with an upward orientation. Let the surface…

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Q: (c) 2x1 + 2х2 - 4x3 = 14 3 = X3 8 X2 + 2x3 = -1 3x1 + X2 + 2x1

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Q: 2 Find the area of the portion of the paraboloid x=9-y²-z² that lies above the ring 1 ≤y² + z² ≤ 9…

A: Given, The paraboloid y = 9-y2-z2  above the ring 1≤y2+z2≤9 in the yz plane.

Q: Part 2 -45 + 7(x + 2) - 6x (no justification needed) = -45+ (7x + 14) - 6x = -45+ (14+ 7x) - 6x =…

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Q: =) x1 + x2 + 2x3 + 2x1 + 3x2 + 6x3 + 3x2 + 4х3 + Х2 — Хз X3 - X1 6x4 = 11 19x4 = 36 15 28 6x4 = -12

A: We solve given system of equations by elimination method.

Q: 7. The nth partial sum of the series Σa is given by S 11 n 12-1 Find the 7th term using the sum.…

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Q: Let f, g: R→R be defined by f (x) = {4x + 1 , if x ≥0,    x , if x < 0} g(x) = {3x , if x ≥0 ,  x +…

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Q: Approximate the stationary matrix S by computing powers of the transition matrix P shown below.…

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Q: 14. Identify any dictator and all dummies in the following the voters in the order listed are A, B,…

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Q: Theorem If f is integrable on [a, b], then where Ar= | f(x) dx = lim Σ f(x) Δx b-a n and x₁ = a + i…

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Q: change 2/2 0 integral b of coordinater 5125 0 125-x2 x y dydx

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Q: 2x1 -X1 + 3x1 + X2 - X3 = 3 2x3 = -8 X3 = 0)

A: We solve given system of equations by elimination method.

Q: A vector field is given by F = ((1 + xy)exy, x2exy). Compute the integral of the vector field over…

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Q: Suppose that 8 people check their coats in a checkroom. If all claim checks are lost and the 8 coats…

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Q: Selve the given initial-value problem in which the input function g(x) is discontinuous. (Hint:…

A: Laplace transformation of the differential Equation