16. Determine lim f(x) if the given function is x→2 f(x) = { 1², I 8-2x, if if x < 2 I x> 2

Q: 2. Coefficients Linear in Two Variables (3x + 2y + 7)dx+ (2x - y)dy=0

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A: A vector space V together with an inner product is called an inner product space. For example: V=ℝn…

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A: we have to use diagonalization theorem to find the eigenvalues of A and a basis for each eigenspace.

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Q: 2 Total differentials Question 1: What are the total differentials of the functions • f(x, y, z) =…

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Q: Let ƒ: R² → R² be an isomorphism where ([-])-[²] and f([:]) = [] = Find f ¹ƒ( [7¹]) X 0 2 2 0

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Q: -C-(F→C), ~C.. ~F

A: Since you have asked multiple questions we will solve the first question for you. If you want any…

Q: Choose all sets that are countable: O [-0.5, 11.5] nz EN} □ 1 n+1 ONU{-1} O(-0.5, 7.5) □ {3k|k € Z}

A: I have given the answer in the next step. Hope you understand that

Q: Explain how the idea of Riemann sums can be extended to approximating f f(x, y)dA. R

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Q: Exercise 2. Consider F(X, Y) the space of all maps f: X→ Y from the set (Y, d). For f,g: X→Y, define…

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Q: Use diagonalization -3 -6 1-7 1. X'= = 2 5 4 to solve the given systems. 21 2 X 4 2. x' = [² ¹/^]x…

A: A=-322-652-744∴A-λI=0⇒-3-λ22-65-λ2-744-λ=0⇒-λ3+6λ2-11λ+6=0⇒λ-1λ-2λ-3=0⇒λ=1,2,3 For λ=1…

Q: 27) Determine whether the following series converges: 1 1-4 (k-1)² k=4

A: There are many tests by which we can show that the series converges. We shall use the famous…

Q: (8) Discuss but no need to submit. Let g = Σ₁" Approximate g to within 0.01. How n=1 many terms will…

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Q: readable/legible solution to the problem be provided .

A: Given: The given integral is I=∫-∞∞x2x4+1 dx. To Find: We have to find the given integral using the…

Q: 5 The inverse Laplace transform of F(s) = 5² - 2s+5 1 f(t) = 5e²¹ sin 2t f(t) = 5e¹ sin 2t 5 f(t) =…

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Q: (4) Let f(x) be the function with domain R given by the rule X if x EQ, and 0 if x # Q. f(x) = = (a)…

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Q: (b) Let C₂ be the contour from 10 + 10 i to 5/8 which consists of an anticlockwise arc of the circle…

A: Given the contour is from 10+10i to 58. The path is on a circle anticlockwise with center at (0,0)…

Q: 5. Use a power series to approximate the definite integral to 6 decimal places. 0.1 a. 50.211 dx b.…

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Q: 2x² - y² lim 2 (x,y) →(0,0) x² + 2y² y√x lim (x,y) →(0,0) 3x + y²

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Q: Find the orthogonal trajectories of the family of curves. Graph several members of each family on a…

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Q: © Evaluate the following complex integral functions, Ş In Z c (Z - A) ² @SZ ² +8 0.52-1.5 dz, where…

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Q: 20 3m Bach ſa Dr. Hy m 1 x+1 where yzx is one. solution of .bama... DE

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Q: For each of the systems in Problems 1 through 12: (a) Find the eigenvalues and eigenvectors. (b)…

A: Given a system of differential equation  dxdt=12-5-1x To Find : a) The eigenvalues and eigenvectors.…

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Q: is Q:- show that the space x = [0₂e) complete space, where e= exponential nat je c= 2.71898

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Q: 2 Find the complete Solution of y + y = 0·001 X² ý (0) 15 = y(0) = 0 ;

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Q: успЈ where /_g[n_1] + n[n] 2 x[n] = (!) u[n]

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Q: M-(NO), -N-P, (M-P)→(O v-Q). ---Q

A: The main objective is to check the validity of given argument by using reductions and absurdum…

Q: cos²x = 3 sin² x 1 = 4 sin² x cos²x = 3 sin²x = sin²x 1-sin²x = 3 sin² x + = sin x is true at x…

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Q: Please do B and C

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Q: 3 1+x 그 |-x

A: Inequality: A mathematical expression in which both sides are not equal. We use &lt;, ≤, &gt;, ≥ to…

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Q: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Use one of the formulas in (5) to find the area under one arch of the cycloid x = t - sint and y =…

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Q: [a] z = dz dr D 4+4-³ P d/y +2 = (4+48-8³) a (x³/2) - 83/2 d (4+48 -√3) (4+48-83)2 3 (4+48-8³) 50 -…

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Q: 3. Find the minimum diameter and the minimum thickness of each yoke that will support a load P-90 kN…

A: We will find the minimum diameter and the minimum thickness of each yoke that will support a load P…

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Q: Find the orthogonal trajectories of the family of curves. x² + 2y² = K² Graph several members of…

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Q: Find a geometric power series for the functions, centered at c = 0 unless a different c is…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find the value of w = 5 bounded by y = 0, y = 2,0 ≤x≤ 2y, and x ≤z≤y + 4.

A: We have to find the value of w=5. It is bounded by:y=0, y=20≤x≤2yx≤z≤y+4

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Q: Let T: R³ → R³ be the linear transformation defined by T((x, y, z)) = (x+z, −y — z, 2r+y+3z). a.…

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