Let {V₁,..., Vn} be a spanning set for an inner product space V. Suppose that x and y are such that (x, v₁) = (y, vk) for all k. Prove that x = y.

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A: (.)  Given iterated integral is,       where we will find the value of

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A: (.) Given,  and  (.) Lagrange polynomial for the function  with  data points  is given by,

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A: The temperature distribution  is governed by the one dimensional heat equation…

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A: Given equation of ellipse

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

Q: Determine whether the improper integral 9 it converges. a. 100 b. 2 C. -1820 50 d. 22 11 9 e.…

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Q: 5. LADW #5.1.9: Recall the p-norms and max-norm, defined on R2 by: ||x||p = (|x₁|P+|x₂|P)¹/p ||X||∞…

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Q: Let f be Continuous on the interval [0,1] to IR and such that f(0) = F(1). Prove that there exists a…

A: This follows immediately from the intermediate value theorem.

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A: Given Information:Demand and Supply functions are provided as:To find:a) Write the matrix .b) Use…

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Q: The graph of f(t) is given below. 765 4 7₁ 6 5 y 3₁ 2 1 t o 10 Find the Laplace transform F(s) =…

A: The given graph has 4 stages.       First stage:      for         Second stage:  The…

Q: 4. Use variation of parameters to find a particular solution of the DE y" - 4y' + 4y = 21 and then…

A: Given differential equation Note: According to the guidelines we are allowed to solve one question…

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Q: You are holding one red sock. In your sock drawer are 4 blue socks, 2 green socks, 8 white socks,…

A: We are given that, in a socks drawer Number of blue socks = 4 Number of green socks = 2 Number of…

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Q: A blood test for diabetes gives a positive result with a proportion of 0.18 when an individual has…

A: Given that :A blood test for diabetes gives a positive result with a proportion of 0.18 when an…

Q: Let c(t) = (cost, sin(2t)). a. Make a table for the parametric curve using t = {0,7,7,7,7,7,7,7, 2n}…

A: The given parametric curve .The aim is to find the values of  and  using the given values of  and…

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A: Suppose that the  length of the  lake  is  ftFrom the  given figure suppose  that  the  given…

Q: 5. Find the volume of the box with length a, width b and height h by setting f (x, y) = 1 and = SSS…

A: We have to find the Volume of the box with length a, width b and height h by setting  and…

Q: 2. now clearly sketch as well as indicate your angle and you may assume you know the points on the…

A: Reference angle is the positive acute angle between the terminal side of the angle and the x-axis.

Q: The system of first order differential equations: has solution: yı (t) Y₂ (t) = e2t (4 cos 2t + 5…

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Q: Suppose our recursive formula for a power series solution is a2 a3 Find the following in terms of ag…

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Q: (a) Convert the point whose polar coordinates are (4, 57/4) to rectangular coordinates. (x, y) =…

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Q: Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros…

A: First we find a root and then use division algorithm

Q: + G = + = n n 1+ + + n 1+ n² - 1 – n

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Q: 4. In the usual topology again, is locally compact? 5. Deduce. {(0, 0)} U {(x, y) = R²; x >0}

A: The given set is, .Locally compactness means that each point in the set has a compact neighborhood.

Q: 3. Compute the flux of F = (2,3,1) through the torus parametrized as r(u, v) = ((2+ cos v) cos u, (2…

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Q: Let I:= [a,b] and let f: I - IR be a continuous functioN ON I such that for each X IN I there exists…

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Q: Follow the steps to solve the below differential equation using series methods. Assuming the…

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Q: Prove that if n is odd then 3n+ 7 is even. Show that if n is an odd prime number it is not…

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Q: #9: Consider the following differential equation. (1 + 3x²) y'' - 8xy + 6y = 0 (a) If you were to…

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Q: Determine the maximum and minimum values of quadratic form Q(x) subject to the constraint xx = 1.…

A: subjected to constrain

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Q: Evaluate the definite integral. [In In x³ dx

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Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure:

A: Here is the problem. the limits of x and y of the given triangle.As x limits we have from 0 to 4.Y…

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Q: Consider the vector field F (x, y, z) = (3z + 4y)i + (z+4x)j + (y + 3x)k. a) Find a function f such…

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Q: . Consider the following non-linear system of differential equations x'=xy- 2, y = x - 2y. Note that…

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Q: Suppose Q is the quadratic form below The minimum value of Q subject to ¹ = 1 is Q = 4. An…

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Q: Find the vertical, horizontal, and oblique asymptotes, if any, of the given rational function.…

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Q: In each of Problems 12 through 15, use integration by parts to find the Laplace transform of the…

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

Q: 2. Let T: P₂ (R) → P₂(R) be defined by T(p)(x) = p(0) + p(1)(x+x²). (a) Prove that T is…

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