4.2. Let a=for n23 (a) Let f be the function given by f(x) = -1/ For x23, fis continuous, xlnx decreasing, and positive. Use the integral test to show that En-3 an diverges. + 3ln3 4ln4 5ln5 (b) Consider the infinite series E-3(-1)"+¹ an = Identify properties of this series that guarantee the series converges. Explain why the sum of this series is less than 3 nlnn (c) Find the interval of convergence of the power series 3 (x-2)+1 Show the analysis that leads to your answer.

Q: Given that f(z)=z-ż where does f'(z) exist

A:

Q: Which of the following must be true in order to use the laws of logarithms in order to simplify…

A: Sol Log is written as :-logab So, in order to use law of logarithm , in order to simplify expression…

Q: Given the following initial-value problem: dy dt di² y(1.5)=1. y'(1.5)=1. Determine numerically the…

A:

Q: Consider the model dP dt where P(t) represents the size of the population at time t. = 5P + 10P²,…

A:

Q: The classroom has the dimensions shown: 729 808 9.1 m 10.3 m 3.2 m 1) Mrs. Congello would first like…

A: We have to find the amount of paint required to paint the walls of the classroom. It is clear that…

Q: A monoply box that has twice the the awichth me twice the length with a volume of 10000 cm³ Find the…

A:

Q: The owner of an apple orchard has field of new trees that are growing and producing more apples each…

A: We need to use the formula: g=a·b to determine the average growth rate.

Q: Find an equation of the line in parametric form that passes through the vertex of the paraboloid…

A:

Q: How many terms of the Maclaurin series for ln(1 + x) should you add up to be sure of calculating…

A: The Maclaurin series of ln1+x is ln1+x≈x-x22+x33-x44+x55-x66+x77-x88+x99-…. The absolute error, ε is…

Q: = [ -- |- 1 AB CA 2 4 6 3 1 1. Find 3A - 2B. 22 0 1 -2 - -2 7 AC 3 CB 3. Find the products DA and…

A:

Q: If y, and y₂ are linearly independent solutions of ty" + 4y + (3 + t)y = 0 and if W(y₁, y₂)(1) = 2,…

A:

Q: develop a curriculum for a university for accreditation as an ICT coordinator to offer mathematics.…

A: Need and Significance of the study:- The scenario of the classroom is changing. There is a…

Q: Find the indicated limit. Note that l'Hôpital's rule does not apply to every problem, and some…

A:

Q: What interest rate was applied if a loan of ₱65,468 will amount to ₱125,000 borrowed for 2.5 years…

A:

Q: How many solutions are there between planes P₁: 2xy + 2z = 2 and P₂: -x + 2y + z = 1? If there…

A:

Q: Density of a plate p (x, y) = x + 2y (g/cm2 ) is given as. R zone in zone 1 y = be the region below…

A:

Q: Group A1) Consider the succession (an) defined by; an = 379an-1-378an-2, n22 and ao = 0 e a₁ = -377.…

A:

Q: Use the method of variation of parameters to solve the initial value problem x'=Ax+ f(t), x(a)=x₂…

A:

Q: Let R be the relation on N defined by R = {(n, m) EN x N: m=n+1). Then R is surjective. True False

A:

Q: let a be a nonempty compact subset of R and let B be a nonempty closed sub set of R such that A…

A:

Q: Recast the system of higher order differential equations as a first order system. u""=2u-3v…

A: The given higher order differential equations are: u'''=2u-3vv''=3tu'v'-cos u Recast the system as a…

Q: How long will it take money to quadruple with continuous compounding at 12% interest? 15,019 72 Ob…

A:

Q: 1. Find the T.F of the following sys.: 園 = -5 3 =][*] + € y = [12] u

A:

Q: The Bar graph below describes the scores of a group of students on a 10-point math quiz 10 9 1 Quiz…

A:

Q: Solve the related phase plane differential equation for the given system. =x²-5y-8 4x³-2xy 9|29|9 An…

A:

Q: Write a dual program such as LP below:

A:

Q: Even though the limit can be found using the theorem, Limits of Rational Functions at Infinity and…

A:

Q: Prove that Let p be a prime. Then (p−1)! ≡ −1 (p)

A:

Q: 9) L [sec Lh sech2t + sinh 2t tanh 2t

A:

Q: xample: Solving Axb, Ux = c, and Rx = d 1x1 + 2x2 + 3x3 + 5x4 Ax=b is 2x₁ + 4x2 + 8x3 + 12x4 = 3x₁ +…

A:

Q: Calculate the indicated Riemann sum S3 for the function f(x)=x²-8x-9. Partition [0,6] into three…

A: Given function is fx=x2−8x−9 and let c1=0.5, c2=2.8 and c3=5.3. We have to calculate the indicated…

Q: At Compute the matrix exponential e for the system x' = Ax given below. x₁ = 37x₁ - 36x₂, x 2 = 34x₁…

A:

Q: 27.12. There can be asymptotic normality even if there are no moments at all. Construct a simple…

A:

Q: A = 24 0 1 01 4 -1 3

A: In order to calculate the eigen value of the matrix A, we need to solve the equation: A-λI=0 for λ.…

Q: 4 - Investigate Interaction of Two Planes Plot the following and their normal vectors. 2x-2y + 2z =…

A:

Q: 2. Use ratio test to determine whether the following series is convergent or divergent: (2n)! Σ n.…

A:

Q: Atwood's Machine. A 15.0-kg load of bricks hangs from one end of a rope that passes over a small,…

A: Given Atwood's Machine. A 15.0-kg load of bricks hangs from one end of a rope that passes over a…

Q: Use the Laplace transform table and the linearity of the Laplace transform to determine the…

A:

Q: The 14 digits of a credit card are written in the boxes shown. If the sum of any three consecutive…

A: Shown are boxes which corresponds to the 14 digits of a credit card.   Also given that the sum of…

Q: QUESTION 3 Let A={1, 2, 3, 4) and B=(-1, 0, 2, 4, 5), and R = {(1,0), (1,2), (3, 1), (4,4)). Then R…

A:

Q: Q2/1 x = 0; pi/100 : 2 Pi; Y₁ = Sin(x) 2. Sin (X-0.25); 83 Sin (X-0.5); ун Y₁ = Cos (x); plot the X…

A:

Q: Compute the definite integral T/4 0 5 sin² (3x) dx

A: Sol:- ∫0π45sin23xdxTake the constant out:  ∫a·fxdx=a·∫fxdx=5·∫0π4sin23xdx=5·∫0π4121-cos6xdxTake the…

Q: 18. Over a period of one week, the Dow Jones Industrial Aver- age (DJIA) did the following: On…

A:

Q: xp z/1 (1 − 1-x7)x^ S 4.

A:

Q: Using Lagrange's interpolation formula, find a cubic polynomial which approximates the following…

A: Let x0,y0, x1,y1, x2,y2 and x3,y3 be the given data. To obtain the Lagrange's interpolation…

Q: Find the length of the following three-dimensional curve. r(t) = (2+5t,9-3t, -6+3t), for 1st≤4

A:

Q: Q/Find half-range sine and cosine expansions of each of the following functions : 0 ≤ t ≤ 1 1≤t≤2 7…

A: We have to find the half-range sine and cosine expansions of the given function ft=t0≤t≤12-t1≤t≤2

Q: Given the scalar functionf (x, y) = 2xy, calculate the line integral along the ellipse curve ²² +²²=…

A: We have to find the line integral along the given curve.

Q: Solve the initial value problem below using the method of Laplace transforms. y' + 3y' - 18y = 0,…

A:

Q: Solve the following equation uxx + Uyy = 3x - 5y with the conditions for the square plate u(0,y)=0…

A: