Problem 10. Prove that for any r ER, there exists a sequence of rational numbers that converges to r, and there exists a sequence of irrational numbers that converges to r.

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A: Given That : system of First order differential equation x'(t)=Ax(t) where A=011011002 a) Find the…

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Q: Given T→(π)=⟨0,−4/5,3/5⟩ , find an original v→(t) function that looks like a circular spiral or…

A: Given, Tπ=0,-45,35 The Original spiral function is to be determined.

Q: Write two proportions so that the product of the extremes is 24.

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

Q: n For each n EN, consider x == with x ER+. Define the sequence {gn} by x 1 8n(x):= f(xn) (a) Find…

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Q: 5. Use Theorem 5.10 (Section 5.3 in Vol. 2 of OpenStax Calculus) for this problem. How many terms of…

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Q: Q5) Given A = 0 – 2    4 determine if x = (1,1,0) is an eigenvector, why or why not?…

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

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A: Introduction: Parametric form is another representation of curve in Euclidean geometry. Here, the…

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Q: Let f(x, y, z) = 9 (√x² + y² + 2² where g is some nonnegative function of one variable such that…

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Q: For items 1-10 Mamada has four provinces namely, Aba, Kada, Ega, Haila with population size of…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: 8-3) het alb below as follows y and the region. , x² + y² = a ² L 2. R= {(x,y) 62² | x² - y² ≤ ²,…

A: Given :   R=x ,y∈ℝ2   x2+y2≤a2 ,x2a2+y2b2≥1 , y≥0  To Find : ∮ y1+xdx+x1+ydy  =∬Qx-Pydx dy

Q: X 2a à 2a a y

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Q: 1 Find the first 10 terms of the sequence an = an-1 Its 9th term is Its 10th term is and a1 = 14. =

A: Given sequence is  an=1an-1 Given a1=14 We need to calculate first 10 terms of the sequence.

Q: 2. Use f(x) = 2x + 5 and g(x) = x^2 + x - 6 for following combinations. A. (f+g)(x) = B. (g-f)(x) =…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Find the linearization L(x, y) of the function f(x, y) at P0 Then find an upper bound for the…

A: We need to determine the linearization of the function: f(x, y)=xy2+ycosx-1 at P01, 2 over R:…

Q: -{(8 Let R=< a-b b : a, b ER . Endow R with the standard matrix addition and multiplication…

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Q: 38. f(x, y) = ln x + ln y R: |x-1| ≤ 0.2, at Po(1, 1), y - 10.2

A: 38 Given function is fx,y=lnx+lny at P01,1. And R:x−1≤0.2, y−1≤0.2. We have to find the…

Q: Combined test scores were normally distributed with mean 1496 and standard deviation 341. Find the…

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Q: Players A, B, C, and D are dividing an estate using the Method of Sealed Bids. There are three…

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Q: For each of the following SEQUENCES, select whether they converge or diverge; for each that…

A: Disclaimer:  Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Someone input a 5 and the output was 2 for a square root function. a) Create a square root function…

A: Given That : Function f(5)=2 To Find : square root function  "As per the policy, only the first…

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A: Given function is f(x) = 3x8x-151-1-8x15832-x110001

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Q: Ex3 i) ii) Let T: C ([0,1]) → R f → f(0) If C ([0,1]) is equipped with the sup-norm, show that T is…

A: As per the policy, we are solving first question. Please repost it and specify which question is to…

Q: Determine whether the series converges or diverges. 8 2 Σ (1 + ²)²³0² e n = 1 converges diverges -…

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Q: Clearly state: True or False If True, provide a concise explanation If False, provide an explicit…

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Q: A tumor is injected with 0.9 grams of Iodine-125, which has a decay rate of 1.15% per day. Write an…

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Q: Consider the following problem; max f (x₁, x₂) = -x2² - x² subject to (x₁ - 1)³ ≥ x² Check whether…

A: Introduction: When assessing whether a multi-variable function is optimal, the quadratic surface…

Q: Question 1. Let x₁, x2, x3 be solutions of the following ODE t²x"" +2tx" + x' +2022x = 0 for t> 0.…

A: 1. Let x1, x2, x3 be solutions of the following ODE t2x'''+2tx''+x'+2022x=0 for t&gt;0.   Also given…

Q: For each nN, consider x,, H (a) (b) 71 X with x E R. Define the sequence {gn} by 8n(x) = f(x) = 1…

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Q: b) Find the absolute relative approximate error for the second order polynomial approximation.

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Q: Let (z-a)" dz where a € C and the parameterization of the curve is a = {|z| = r}. Apply the…

A: Hint: The statement of fundamental theorem  of complex analysis is: If a continuous function f has…

Q: QUESTION:  Given a 2-dimensional function T(x,y)=4y2+sin(pi*x)T(x,y)=4y2+sin(pi*x) answer the…

A: Note: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 5² (2²-10x) dx write the integral using the limit and som formula de finitier of the integral in the…

A: Given That : ∫05(x3-10x) dx To Find : integral in the form of the limit of the sum

Q: a b с d e f a b c d e f cdf a b e d e f a ecdb a b fc a b c d e f b f Answer: deca ecbfad Enter a…

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Q: 4. [- Find two power series solutions of the given differential equation about the ordinary point x…

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Q: Using the formula f(x+th)-f(x) t f'(x)= lim: h→0 and admitting the existence of the derivatives of…

A: a) f:R3→R2 defined by fx,y,z=x2+y , x+y+z2 also given z=1,1,2 , h1,1,2 using the formula…

Q: Given: X 057 8 10 f(x) 02 -1 -2 20 a.) Determine the value at x-5.3333 seconds using quadratic…

A: The table of values given is as follows: x 0 5 7 8 10 fx 0 2 -1 -2 20 (a) We will first find…

Q: Jo 1 (x+8)5/3 dx

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

Q: 3.17 Let f(t) be a T-periodic signal and let g(t) be the signal given by 1 g(t)= == t-a f(u) du.…

A: Introduction: Periodic function is a very significant function in mathematics and many applied…

Q: A curve is defined by y = 8 x² + 2 I. Find the turning points of the curve using differentiation.…

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Q: ***BELOW ARE TWO DIFFERENT QUESTIONS, PLEASE SOLVE EACH SEPARATELY AND SHARE ANSWERS FOR BOTH.…

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

Q: ILS] Demonstrate how any vector x € R³ can be expressed as a linear combination of the following…

A: Given Data: e^ie^i=0, i=1,2,3e^j=1,∀ j≠i x2=2-30