Use the binomial theorem to expand the binomial expression below and state the range of values of x for which the expression is valid (1+x)^-3

Q: *? Let (sn) be a sequence that converges. (a) Show that if sn > a for all but finitely many n, then…

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Q: 3. Mr. Francis worked on a regular holiday that falls on his rest day. He rendered 12 hours of…

A: We have to find the amount which Mr. Francis should receive as the gross pay.

Q: Please use Laplace Transform Method Consider the following IVP: y"-10y' +9y = 5t, y(0) = -1, y'(0) =…

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Q: (4) Consider the constant rate of decrease of a certain microorganism. At the start, there are…

A: We have to find the number of microorganisms that will be there after 45 seconds.

Q: Find the inverse of laplace, f(t) if: 4s + 12 s3 – 9s2 + 23s – 15 5. F(s) : - -

A: Given: F(s)=4s+12s3-9s2+23s-15 To find the inverse Laplace transform

Q: 5. Identify and sketch the graph of the following equations in R³. (a) a2 + 4y? + 22 – 8x + 16y – 2z…

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Q: Find the inverse of laplace, f(t) if: 4s3 + 12s? 6. F (s) %3D (s – 3)4 -

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Q: Give an equation of a plane described below. Determined by intersecting lines L1 and L2 L1: x = 2t y…

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Q: Show that F (x, y) = x2 + 3y is not uniformly continuous on the whole plane. Hint: You must prove…

A: Here, we are given the function F(x, y)=x2+3y. Now, we need to show that the function F(x, y) is not…

Q: Let f(2) = z2 + 2|2|2 + z where f is differentiable. Determine the set of all points zo where f is…

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Q: Please use Laplace Transform Method Consider the following IVP: y" -10y' +9y = 5t, y(0) = -1, y'(0)…

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Q: If E is the solid described below with density function P(x, Y, 2) = x + y, find the following…

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Q: Find the solution. (x+e") dy – dx=0 A y=ce' +xeY B) x=ce' + ye* x=ce" + ye" D y=ce*+ ye

A: As per our guideline we are supposed to answer only first asked question.Kindly repost other…

Q: Define the function zlm(z) z +0 f(2) = Z = 0 1. Prove that f is continuous at the origin. 2. Prove…

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Q: -3 Are the vectors -3 -4 -8 and linearly independent? -6 3 linearly dependent If they are linearly…

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Q: Determine the general equation of the plane N passing through the point P(3, –1,2) and parallel to…

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Q: Consider the following facts: The members of the Elm St. Bridge Club are Joe, Sally, Bill, and…

A: The members of the Elm St. Bridge Club(ESBC) are Joe, Sally, Bill and Ellen.          Answer:…

Q: Let X = {-2, 0, 2} and let P(X) be the power set of x (the set of all subsets of X). A relation R is…

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Q: During an iteration of bisection method for solving f(x) = 0, we got f(2) = -6, f(-1) = 2 and f(-4)…

A: The equation in the form f(x)=0 is called a transcendental equation. Geometrically the solution of…

Q: f(2022) (0) 3) Solve for the following equation: The Maclaurin series expansion of tan-r is given by…

A: We have to approximate the 1/2 arctan(1/2).

Q: Determine one real root of h (x) = In() = -3 between -0.9 and –0.2 using the Bisection Method.…

A: Given, h(x)=lnxx3-8=-3    ; -0.9,-0.2h(x)=lnxx3-8+3=0To find: One real root of h(x) between -0.9 and…

Q: b. Consider the graph of function f below. 1,5) | (7,9) (-1,-1) (4.2) (1,-1) Complete the following…

A: The given graph is

Q: 1. Find the radius of convergence and interval of convergence of the series n(x+2)" 5n-1 n=1

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Q: The elementary matrices in sequential order that converted a coefficient matrix, A of a system of…

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Q: 1. Consider the shaded area below the graph of the function y = x² + 1, above the x-axis and between…

A: We will use Riemann sum to find area under curve y=f(x) in the interval x∈a,b Area ≈Δxfx0…

Q: Sketch the region (Use Calcchat.com) and provide a picture. Write the an equivalent integral with…

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

Q: Use Poner Series Solutions to find the recurrence reQation andl the first three non-zero terms forr…

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Q: Identify and sketch the graph of the following equations in R z = 1 – e"

A: We will have to sketch the graph of z=1-ex in ℝ3.

Q: 1. Consider e" = for all r € R. n! n=0 a. Determine the power series representation of f(x) = xe =…

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Q: Activity #3 in Differential Equations Solve for GS/PS for the following differential equations.…

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Q: 7. For the Lorentz matrix P = use a? – 32 = 1 and v = B/a to verify that a = 1/vi – v² and 3 = v//1–…

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Q: Use the tables of Laplace Transforms to find the inverse Laplace Transform : F(s)= 2 s² +35-4

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: Allen Electronics manufactures two types of computers- desktops and laptops. The production of a…

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Q: Compute (n) where o is the Euler's Totient function. Show your work in the space provided. 1. ø(8)…

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Q: Do the following for the function beloW. f(x) = V1+ 3x %3D a) Use the binomial series formula to…

A: We have to find the maclaurin series for f(x) using binomial series formula.

Q: (1) Show that planes perpendicular to the r-axis have equations of the formr=a sec 0 in cylindrical…

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Q: Use substitution method

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Q: 3. Reduce each fraction to its lowest terms. If it is already in lowest terms, writé "not possible".…

A: To reduce each fraction to it's lowest terms.

Q: Please help me find the sum or divergence with telescope methods

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Q: 2) 18.49 19.9 4) 4.63 4.3 6) 10.35 10.35 8) 25.6 25.9

A: (2) 18.49 = 1849/100        19.9 = 1990/100        Since, 1849 < 1990                  =>…

Q: Find the volume of the solid that lies below the sphere z + x- + y- = 9 and above the cone z =/3x2 +…

A: To find volume we will use spherical co ordinate system and for cone we will use cylindrical co…

Q: Find the inverse of laplace, f(t) if: 10s + 20 11. F(s) = (s + 3)(s² + 4s + 8) 2

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Q: y(4) + 2y" + y = (x – 1)²

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Q: 1-Let B be the set of all infinite sequences over {0, 1}. Is this set countable or not, prove it?

A: Please post the multiple parts separately.Here I answered the 1st question as per our policy.

Q: 1. A power series is a series of the form and Cn's are where x is a

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Determine whether the pairs of functions: f1(x) = e^(3x) and f2(x) = e^(-3x) are linearly dependent…

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Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

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Q: 5. Find the absolute error and relative error for values given below: (a) Let x = 2.7182818 and x'=…

A: According to the guidelines I am answering first question which appeared first (question number 5)…

Q: Consider the following IVP: y"-10y' +9y = 5t, y(0) = -1, y'(0) = 2 Find the general solution. 5 50…

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Q: if m varies directly as n and the square of r and inversely as s if m 40 when n = 5 r = 4 and s = 6

A: Let us consider the statement a is directly proportional  to b means a∝b To make the equation use…