Why did we plug in x = 1/2 at the last part of the solution for the second problem

Q: – 2z = 3 and 2x – y +z=-13. Find the following. Consider the planes x – 1. The cosine of the angle…

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Q: 1. a) For 0<x<1, show that /2 1+ x b) Use the estimate in a) and integrate it to prove that 1 1 -dx…

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Q: Using the Bisection method, find z5 and z for f(2) = e - 4/z. Use z5 2 = 1.8. 0.9 and

A: Given f(z) = ez - 4z

Q: Q2: Use two iterations of N-R method to solve the nonlinear equation with estimated solution Xo =…

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Q: The eigenvalues of a 4x4 matrix, A are 9, 4, 4, and 1. Execute Gram-Schmidt process on the following…

A: Eigenvalues of A and inverse of A

Q: Give the detailed solution on the differential equation. (1st order and 2nd order) 1. √x (y')² - (√x…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: Direction: Determine the Inverse Laplace Transform of the functions by reduction to partial…

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Q: Problem 1 Find the distance d(v, W) from i= ER' to the subspace W = Span Hint: First check if W has…

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Q: Use the given transformation to evaluate the integral. | 5x2 dA, where R is the region bounded by…

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

Q: Use the fact that matrices A and B are row-equivalent. 1 2 1 0 2 5 1 A = 3 7 2 7 15 6 -2 2 -2 6. 1 0…

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Q: Use the De Moivre's Formula Prove: Express tan 40 in terms of tan e.

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Q: Find the Taylor series for f(x) centered at the given value of a and the interval on which the…

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Q: Is it true that Arg(z) = arctan for x + 0, where x = Re(z) and y = Im (z) ?

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Q: -3î + (4 + m)j – k ,č = -9î + 12j – (3 + m)k , ,Q %3D (5 + т,4,0 + m) аnd P %3 (-1,4 + т, —3). Find:…

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Q: Find the form of the cubic function that has  a x-intercepts 5, 2, -3 and y-intercept 30

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Determine the coefficient of the 5th term of the Maclaurin series expansion of f (r) = cos a 12 10!

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Q: Which of the following cannot be defined as an inner product between two vectors (x0, Yo) and (¤1,…

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Q: トン メ+??-9 zy +3=8 4X -3y =-2 Ans / X=1 ウ-2?こ4

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Q: 1 Find the Inverse Laplace Transform of s2+2s + 10 A -e 'sin9t 3 -e-'sin3t 3 3t e"cost (D 3 "cos3t…

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Q: The three series An, EBn, and Cn have terms 1 An = n8 1 Bn 1 C, = n4 ' n Use the Limit Comparison…

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Q: find the value of f(x) at x 10:

A: Given, x 9.3 9.6 10.2 10.4 10.8 f(x) 11.40 12.80 14.70 17.00 19.80 To find the value of f(x)…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: To find the distance from point P to the line AB .

Q: If fn converges point wise to f on a closed and bounded set then the convergence is uniform.…

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Q: Let f) = x* +x + 2x² -1€ Z,lx). Then x =1 is a root for f(x) of multiplicity: 2 4 None

A: Given that fx=x5+x3+2x2−1∈Z3x. We have to find the roots of multiplicity of fx at x=1. At x=1…

Q: Let F be a commutative ring with identity and let f (x) E F[x] be a polynomial of degree 4. Which of…

A: Concept: Polynomial with degree 4 have 4 roots. However it is not compolsory that the roots are…

Q: Using the Bisection method, find z, and z for f(z) = e - 4/z. Use z, = 0.9 and = 1.8. %3D

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Q: Denote by C[0, 1] , the space of all continuous functions defined on the unit interval [0, 1]. Show…

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Q: Given: In(1 + x) = En=0 (-1)" n+1 ¡f |x| < 1. 100 n+1 1. Find the Maclaurin series for f(x) =…

A: We have to find the maclaurin series.

Q: 11. Use the Mean Value theorem to show that f(x) = 2x sinh (æ – 1) + 2" – x has a critical number…

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Q: Find a basis for and the dimension of the solution space of the homogeneous system of linear…

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Q: Q2. [2 1] 1 X; X(0) -1 3 Solve the IVP: X' = 1 3

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Q: Lét Y C R² be the set {(x, y)|0 < x < 1,0 < y <1 and y E Q if x # 0} endowed with the dictionary…

A: Given that  Y⊂R2 be the set x,y; 0≤x≤1, 0≤y≤1 and y∈Q if x≠0 So, the set Y can be written as,…

Q: The functions: ƒj(x) = 7x and f2(x) = 2x form %3D a fundamental set of solutions of the DE: x²y" –…

A: (1) Given the function f1x=7x &amp; f2x=2x2 we have to show that these function form a fundamental…

Q: Determine the power series expansion (in sigma notation) of the function f (z) = sin z at z = 0 (2n)…

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Q: Find the solution of h (x) = e sin r = 2 using False Position method between 3.0 and 3.1 (use these…

A: To find the solution by using False position method between 3.0 and 3.1

Q: (i) y' + y = e-3t cos 2t,

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Q: 5. State the definition of the interval of convergence of a power series. Find the radius of…

A: First we will define the interval of radius of convergence. Then we will use the Ratio test to find…

Q: Find the indicated powers of the given complex number. Express the result in polar form, then…

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Q: Let F be a field of 4 elements and let f(X) e F[X] be an irreducible polynomial of degree 4. How…

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Q: Use Lagrange multipliers to find a vector in 3-space whose length is 3 /3 and whose components have…

A: In the equation ∇g=λ∇f, delta represents partial derivative. A partial derivative is a derivative in…

Q: Use the substitution x = e' to transform the given Cauchy-Euler equation to a differential equation…

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Q: Answer the question below: Do not evaluate The student should setup the iterated double integral…

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Q: Find the subdifferential of the following funtion: f(x) = |c' x|, x E R“

A: given clear explanation below

Q: What is the expansion of 1 f (x) = %3D Ο Σε' Σ 2n 2n Σ Next

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Q: 3. Let X be a set. Call a subset A C X to be finitely complemental if its complement is either…

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Q: A plane passes through the three points A(1, 1, 1), B(2, 3, 4), and C(1, 0, 1). Find a parametric…

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Q: Use the Babylonian's formula to calculate the circumferenice of a circle with diameter of 6 units.

A: Circumference of a Circle - Definition The circumference of a circle is the length of the boundary…

Q: Find the maximum of f(x, y, z) = x + y + z subject to the two constraints x + y° +z? = 5 and ¿x + y…

A: Given, f(x,y,z)=x+y+zLet g(x,y,z)=x2+y2+z2=5       h(x,y,z)=16x2+16y2+6z2=5To find: Maximum of…

Q: What is the differential equation of the solution y = C1e 9¤ + C2xe Ya -9x + C3e7¤ ? O y" + 11y" –…

A: To find the differential equation for which the given solution belong .

Q: Find the unit vectors that are perpendicular to U = and V =,

A: Given the vectors U→=2, 3, 4 and  V→=-1, 3, -5 We will find the unit vectors that are perpendicular…