Show that lim (x³ - x) = 6 in the following steps. Do not use derivatives. x-2 (a) Show: if x - 2| < 1, then |x³ − x − 6| ≤ 18.

Q: Find the linear approximation of the function g(x) = V1 + x at a = 0. g(x) = Use it to approximate…

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Q: Maximize 9x2 + 2x3-X5 subject to x1 - 3x2 2x2 x2 + x3 4x4 X4 +2 X5 +4 +3

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Q: 0 --------------] b₂ = 10 a. Find A¹ and use it solve the four equations Ax=b₁, Ax=b₂ Ax=b3, and…

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Q: Prove the following statements. B. Let x EZ. If x² - 6x + 5 is even, then x is odd. C. Let x E R. If…

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Q: (1) Let G = {(ªd) : a,b,c,d € R, and ad- bc = and recall matrix multiplication a (²2)· (22) - (x +…

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Q: We know: d SE= (1.02)2t dt Calculate 8 a) 1.86% b) 2.86% 3.96% d) 4.96% e) 5.86%

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Q: Part 1: What does it mean for a quadratic to “model” a real-world situation?  Can you imagine any…

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Q: Use ordinary induction to prove that C(n) = 2n + 3 is a solution to the recurrence C(0) = 4 and C(n)…

A: To prove that is a solution to the recurrence relation and for all , we can use ordinary…

Q: Prove using the following 1. Direct Proof: The sum of two even integers is also even

A: According to guidelines we can did only the first question.Thank you.1.Direct Proof:The sum of two…

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Q: Read the information below and construct the objective function, and the associated constraint…

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Q: {ne N} is neither open nor closed; 1 Let S = {:n € N} and take xo € S. To show that S is not open,…

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Q: (2) Show that the solution of the differential equation is exact and find its solution. y²– 2x²…

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Q: Obtain all the indicated roots of the number in question. 5. 7

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Q: 5. Show that the solution of the inhomogeneous iVP un - kurz = f(x, t), u(x,0) = o(x), u(x,0) = (x),…

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Q: Determine the Surface área for f (x, y) =13+x2 -y2 on the region R= {(x, y); x2 +y2 ≤ 4

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Q: The figure shows triangle ABC, an isosceles triangle where the base angles LABC, ZACB are twice the…

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Q: Consider the nonlinear system (xi-xi + 2x₂ = 11 (x²+2x₁ + x₂ = 19 When the tolerance value is 109,…

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Q: A local news channel plans a 36-minute Saturday morning news show. The show will be divided into…

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Q: Question 1. Express the following in index notation: (a) ā. B (b) B. ā = (c) A · B

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Q: Given f(x,y) = x^2 + xy + 3x + 2y + 10. Find the critical point(s).

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Q: can you please do (c) and (d)

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Q: The initial tableau of a linear programming problem is given. Use the simplex method to solve the…

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Q: don't understand how phi(a+c)=a+c. Please explain. Thank you

A: Given

Q: 3 max z = 3x₁ + x₂ s.t. x₁ + x₂ = 3 2x₁ + x₂ ≤ 4 x₁ + x₂ = 3 X1, X₂ = 0

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Q: 24. Make a rough sketch of a contour map for the function whose graph is shown. X

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Q: Prove that ·∞ 1 x² + 1 4+ 1 dx is a convergent improper integral. x4

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Q: 0.5 kg/L Pollutant 15 L/min 1000 L Pure Water Tank A 15 L/min Pure Water 5 L/min 1000 L with 5 kg…

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Q: Apply the translation theorem to find the inverse Laplace transform of the following function. 7s +…

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Q: Find the inverse Laplace transform: b. F(s): 5(s+2) s(s²+6s+9)

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Q: The difference of two positive integers is not necessarily positive.

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Q: where did n+1 come from? can you provide explanations for the whole solution

A: To show that∫0∞xn−1e−xdx=(n−1)! implies∫0∞xne−xdx=n! we can use integration by parts, which is given…

Q: y + Y 1+x || -(1 + x)²y5) 2 with y(1) = 1

A: 5. Given that the differential equation is:                                  To find the solution of…

Q: Let G be the graph below. The edges are labeled by integers. a L 1 10 20 8 b 2 1 с 12 13 3 If 18 g…

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Q: (a) State whether the sequence (tn) defined recursively by t₁ = -1, in =l-t3, n22 is an arithmetic…

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Q: (f) If we have two sets A, BCR, A and B are both spottily decreasing, then AUB is also spottily…

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Q: dx dt = 10x − x², x (0) = 1 -

A: 2. Given that the differential equation is                                      To find the solution…

Q: Given a curve defined by the parametric equations (t) = t³, y(t) = t², for t € R, find the curvature…

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Q: b) y" +3y' + 2y = e; y(0) = 0, y'(0) = 3 c) y" +9y = sin(2x); y(0) = 1, y'(0) = 0 d) (4) (0) (0) (0)…

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Q: D. Let A and B be sets. Prove that (A × B) ^ (B × A) = Ø if and only if AnB = Ø. (Use any…

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Q: Let V = {f: R→R: fis continuous}. V forms a vector space under the "usual" addition and scalar…

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Q: Without doing any work, explain why: [15][x2] 5. = has is inconsistent (meaning no solution exists).…

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Q: Consider the following all-integer linear program. 1x₁ + 1x₂ 5x₁ + 7x₂ ≤ 47 1x₁ + 6x₂ ≤ 24 2x₁ + 1x₂…

A: Therefore the 3rd option is correct

Q: 2. Consider the curve r(t) = t - sin(2t) - cos(2t), 1 as 0 ≤ t ≤ π, which I have drawn for you…

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Q: sentences). Is the following linear transformation injective? Surjective? (Justify both with full…

A: The given linear transformation .The aim is to check whether the linear transformation is injective…

Q: Find the positive minimum point of the function f(x) = x^-2 * tan(x) by computing the zeros of f' (…

A: We will use function g(x) in the Secant's method to evaluate the roots where f'(x) is zero.

Q: In a certain city, a car rental service has a fleet of about 5500 cars. The pattern of rental and…

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