Given the sequence defined by the following recurrence relation: a₁ = 2 a=a- for i≥2 Prove that a, for any positive integer n.

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A: Solution is given below Explanation:Step 1: Step 2: Step 3: Step 4:

Q: 8. a) Show that f(x) = kg(x) is quasiconvex if g(x) is quasiconvex and k > 0.b) Show that f(x) =…

A: I gave a clear written solution below, please refer that.Explanation:

Q: 8y'' + 4y' +y = 0 solve for y(0) = 0; y'(0)=1

A: Given differential equation is:8y"+4y'+y=0

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A: Let ϕ(x)=∫a(x)b(x)f(x,t)dtWhere both a(x),b(x) are differentiable functions.Then the derivative…

Q: Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it…

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Q: Problem 2-32 (Algo) Required: Find the after-tax return to a corporation that buys a share of…

A: To calculate the after-tax return for the corporation, we need to consider both the capital…

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A: If f(x) is continuous on  then the improper integral of f(x) over the interval  is…

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A: We have to find the particular solution of the differential equation

Q: 4. Prove that a subset of R is convex if and only if it is an interval. 5. Show that the union of…

A: Please see the explanation.Explanation:4. To prove that a subset of R is convex if and only if it is…

Q: Solve the given initial-value problem. y"" + 6y" + 9y' = 0, y(0) = 0, y'(0) = 1, y"(0) = −4

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Q: U.S. Citizens 65 Years and Older The number of U.S. citizens aged 65 years and older from 1900…

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Q: N Find the general solution of this equation: 9y"+6y'+ y =

A: The given equation is a second order homogeneous differential equation. The general form of such an…

Q: Let p be an odd prime, and let a € Z represent a primitive root mod p. Show that a + tp represents a…

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Q: Sketch the region of integration and evaluate by changing to polar coordinates: For f(x) = √6x x2 L°…

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Q: A3 Use separation of variables to find the solution to the boundary value problem Uxx + Uyy = 0,…

A: That is the  general solution u(x,y) in the given explanationExplanation: please give helpful rating…

Q: USE LATEX CODE,OR TYPE THE ANSWER(3) (LATEX question) Let n ∈ N and take any c ∈ R. Find lim xn −…

A: The limit of the given function as x approaches c is n⋅cn−1.Explanation:To find the limit of the…

Q: Problem #2: Consider the symmetric matrix Го з M=30 0 0 00-4 Find constants c₁ and c₂ such that the…

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Q: Find the equation of the circle that passes through the intersections of the circles x^2 + y^2 -8x -…

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Q: 6. Analyze whether the following sets are convex: Please make the answers step by step as explicit…

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A: Given function is the following : Here is periodic function with period and continuous on .Noted…

Q: (1) Define the function f : RR by f(x) at a 1. 2-x x<1 x2 x ≥1 Show that f is continuous

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Q: (2) Use the definition of limit of a function to find lim x³-3x-2 x+2x2 - 3x+2

A: To find the limit of the function x3−3x−2x2−3x+2 as x approaches 2, it can apply the definition of…

Q: 4. (a) Show that {(2, 0, 1, 1), (-1,2,3, 1), (1,0,2, -1)} is a linearly independent subset of R¹.…

A: (.)  given subset of space  is,           (.) Linearly independent set: A set of vectors  is said to…

Q: Solve correctly all parts

A: The Integral Test is a method used to determine whether a series converges or diverges. It states…

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Q: Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it…

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Q: Determine if the improper integral is convergent or divergent. GRAPH WITH SOME SOFTWARE If it is…

A:

Q: (1) Consider the following LPP: maximize subject to 12 z=x17x2 x3 - 2x4 2x1 1 - - - x1 + x2 11 2 x2…

A: Cycling accursAt this point, notice that the tableau is the same as the initial tableau except for…

Q: 2. Let us remember that the Subgradient Method minimizes f(x) using the following iterative update:…

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Q: aw Find and ду x aw dy at the point (w, x, y, z) = (-4,-1,-1,1) if w=4x2 y2+4yz-4z3 and x² + y²+z² =…

A: 1st Note that the second equation(x2+y2+z2=3) is irrelevant here for the given problems,as w is…

Q: Which of the followingare trees and which are forests?

A: A is a tree B is a forest C is a tree D is a forestExplanation:

Q: Q6. Evaluate (2yx² - 4x)ds, where C is the lower half of the circle centered at the origin of radius…

A: check belowExplanation:Step 1:Step 2:Step 3: Step 4:

Q: Show that the σ-algebra B of Borel sets contains all closed sets

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Q: Consider the initial value problem mx" + cx' + kx = F(t), x(0) = 0, x'(0) = 0 80 modeling the motion…

A: From the given values of m,c,k,F(t), the equation of this model is2x″+8x′+80x=80cos⁡(8t)

Q: e the variation of parameters to solve the given equation: y+y"-4y'-4y=2e* +4e²*

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Let a 7,2,4) and b=(1, -5,-2). Find a vector that == - has length 3a+26 and a direction opposite to…

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Q: (1) Solve the following differential equation Solution: 16d¹y dx4 d²y +24- dx2 +9y= 0.

A: Therefore, the required answer is y=(c1​+c2​x)sin(23​x​)+(c3​+c4​x)cos(23​x​)Explanation:Step 1:…

Q: Real analysis question  Only if you know the concept then solv Don't use chat gpt.

A: The objective of the question is to determine whether the given sequence is convergent. A sequence…

Q: Definethefunctionf :R→Rbyf(x) x2 x⩾1. Showthatf iscontinuousat a = 1.

A: ​f We have proved that is continuous at a=1​Explanation:Step 1:​f:R→R by f(x){2−xx2​x&lt;1x⩾1​​Step…

Q: 50 Unit 3 Computing Truth Values 2. Compute the truth values of the following, using the values…

A: The task involves computing the truth values of three expressions, denoted as \( f \), \( h \), and…

Q: What is the coefficient of 10 in the expansion of (x + 2) 15 + x4(x+3)16? Submit Randomize Reset

A: The required value of coefficient of x10 for the given expression is 472960488Explanation:

Q: 5. Show that the function that sends an ordered pair ((x1, x2, x3), (Y1, Y2, Y3)) of elements in R³…

A: I have write answers below Explanation:

Q: need help

A: For instance, putting x = 1,x2 + x2 = 12 + 12 = 1 + 1 = 2.Thus, The Blank will be filled with…