lim inf (x² − [x]²) x →∞

Q: Let the vector field (x,y)→f(x,y) be l-one-sided Lipschitz in space, let h=0.1, and consider the…

A: We have been given: h=0.1l=-5 Function z=y+hf(x+h,z) We have to find the smallest L number such that…

Q: Consider the initial value problem y'(x) = y(x) V x = (0,5), y(0) = 0. (*) How many solutions does…

A: Given : y'x=yx   ∀x∈0,5  y0=0 To find solution of first step of implicit Euler scheme with step size…

Q: 4. Show that the set S = {ax²+bx+c: a, b, c € R and a ‡ 0} is NOT a subspace of R[x] by showing that…

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Q: : {1, 2, 3, 4, 5, 6, 7, 8} How many subsets are there total? Let S =

A: We have to find the number of subsets, number of odd subsets and number of even subsets.

Q: Investing: Inverse ETFs (Exchange Traded Funds) Inverse ETFs, sometimes referred to as "bear market"…

A: Given, The total amount invested is $13,000. The amount invested in both SH and REW are the same.…

Q: Solve the equation. (x + 9xy¹) dx + ex²y³dy = 0 An implicit solution in the form F(x,y) = C is =C,…

A: The given differential equation is ,        (x+9xy4)dx + ex2y3 dy = 0 (.)  An equation of the form ,…

Q: . Can the equation x + y + z = sin(ryz) be solved uniquely in form = f(x, y) in a neighborhood of…

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Q: Show that 1 - i is an irreducible in Z[i].

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Q: Q9: Using Matrix - Inverse method to find the stream flow rates (F₁, F₂, F3) by material balance as,…

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Q: Show that (up to isomorphism) A5 is the only simple group of order60.

A: Given : G=60 To Prove : G≃A5

Q: 3. Given an integer a, then a³ + a² + a is even if and only if a is even. 4. Given an integer a,…

A: As required in the question, detailed proof of 3, 5 and 9 are given as follows :

Q: Consider the second-order differential equation d²x dx + a dt² dt + b²x = 0 (a, b positive real…

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Q: Find the maximum and minimum values z = 2x y subject to the constraints CHIC TUNICLISTI

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: European

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Q: With the use of the the Second Derivative Test, determine the relative extrema and saddle point(s)…

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Q: Stefan's law of radiation gives the rate of change of dx dt Where x (t) is the temperature (kelvins)…

A: As per our guideline,we are supposed to solve only first question. Kindly repost other question as…

Q: 3-1 1 Let A = 7 -5 1 The eigenvalues of matrix A are... 6-62 A. None in the given list OB₁A₁ = 0 and…

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Q: 1. In this problem, we will use the intermediate value theorem to estimate V12. You may use a…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: 1 x dy -) (3y+--- x dx 2 y 1 y x +(52+-- y = 0

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Q: Problem 2. How many positive integers less than 1000 are multiples of 3, 5, or 7? Explain your…

A: Inclusion and exclusion  principle:        if the first job can be done in 'n' ways and the second…

Q: (a) True or False: The only time ||+|| = |||| is when = 0. You must provide an explanation to get…

A: a. True ||v+u||<=||v|+|u||.This fact is known as the triangle inequality

Q: 2. Find the absolute maximum and minimum values of f(x, y) D = {(x, y): y ≥ x², y ≤ 4}. = 3x² + 2y²…

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Q: # 5 #6 Show that it I an is divergent, then so is Shaw that it I lanti-and < & then convergent. must…

A: Given that ∑n=1∞an  is divergent   We know that       an≤an+an2⇒an≤anan+1⇒anan+1≤an Let bn=anan+1 We…

Q: If X and X are the eigenvectors corresponding to distinct eigenvalues and respectively. then X₁, X,…

A: Explanation of the answer is as follows

Q: (1) Let P: John gets a raise Q: John buys a car R: John invests in Boeing S: John pays off his house…

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Q: Problems 5-6: Find the derivative of the function at the given point in the direction of A. ( 5)…

A: 5. Given,            f(x, y, z)=-2x-7y+8z, (-9, -8, 5), A=3i-6j-2k.

Q: 4. ) Calculate the cost of computing A = uvT where u and v are column vectors of size n.

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Q: 11. Find x and y, if DE is a median 3x⁰ 8y E 6x10y-4

A: The given triangle is DEF With  angle DEF right angle and DE being the median on CF Consider…

Q: In each of the following problems, find the Wronskian W (y1, y2) (x) of the given list of functions…

A: Introduction: The Wronskian is the determinant of the associated matrix. Therefore, only the trivial…

Q: (a) Find the differential of the daily cost and use it to approximate the cost change if the current…

A: Given Cx=x31000-x250+50x+20,000 (a) Differentiate the function with respect to x.…

Q: Question No. 2 2.1 Using the standard list of the Laplace transforms and properties, Find the…

A: Solution of 2.1 The given expression is ft=teb+2tcos2a+3t. Substitute a=0, b=6 in the expression of…

Q: Graph the feasible region for the follow system of inequalities by drawing a polygon around the…

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Q: 3.(a) Show that z8 − 1 = (z − 1)(z + 1)(z − i)(z + i)q(z) for some polynomial q(z) which you should…

A: Given z8-1=z-1z+1z-iz+iqz z8-1=z42-12          =z4-1z4+1          =z22-12z4+1          =z2-1z2+1z4+1…

Q: Suppose >1 and n+1 = 2-1/2 for ne N. Show that (r) is bounded and monotonic. Find the limit.

A: To solve this problem we use principle of mathematical induction and also use  A.M &amp; GM…

Q: A computational system has passwords of either 4 or 5 characters (letter or digit). Note that…

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Q: V. Identify the value/s of x for which the corresponding function evaluation is true. Show complete…

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Q: Solve the following optimization problem: = inf x₁ + x₂ 8.t. +2x = 1 ZER²

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Q: In this part of the solution,r3=38448r3=8r=2, how did we get 2?

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Q: Use excel to solve the following linear program. Max. 3W + 4M s.t -1W + 2M ≤ 8 1W + 2M ≤ 12 2W + 1M…

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Q: 1-2 1 Given C= -2 4 -2 1 -2 1 OAC²(61-C)=0 OBC²-C+61=0 OC. None in the given list OD-61-C³=0…

A: The given matrix is: C=1-21-24-21-21 We have to determine the consequence of Cayley-Hamilton…

Q: Solve the given initial value problem. y'' +4y' +29y=0; y(0) = 2, y'(0) = -1 y(t) =

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: A sensor's dynamics are described by the following differential equation: d'y dt4 +0.2d³y dt³ + 4y =…

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Q: 33. 2 ²² = ( ² ) ² + ( ² ) ² 4 8

A: (29) Given x2+y2-z2=1 n

Q: (a) f(x)= 3c²³-3Jc +4, for JC = 6 f(x) = /noc, for x > 0 Ⓒ 1) 3 1 f(x) = x²³_2x³ + x₁ f(x) = ₁ for x…

A: We used the following results: 1) If f''(x) &gt; 0 then f is strictly convex. 2) If f''(x) &lt; 0…

Q: . Let consider f(x) = x³-3x on the interval [-1,2]. (a) Execute first 2 iterations of Golden Section…

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Q: T 1+2 cos 8 3. Using contour integration evaluate Jo 5+4 cose de

A: The given integral is ,                ∫0π 1+2cosθ5+4cosθ dθ (.)  To solve the given integral of the…

Q: 1. Find formulae for cos(40) and sin(40) in terms of cos and sin only.

A: cos(4θ)=cos22θ-sin22θ⇒cos(4θ)=(cos2θ-sin2θ)2-(2sinθcosθ)2…

Q: 3. So far in the course, we have only talked about sequences which converge to some real number. In…

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Q: Use the following formula. nt (¹)-1] + A= P () Suppose that you drive 50,000 miles per year and gas…

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