Let En be absolutely convergent. a. If yn is absolutely convergent, show that (xn+yn) is also absolutely convergent. b. If yn is conditionally convergent, show that (xn+ yn) is also conditionally convergent.

Q: A mass of 4kg stretches a spring 20cm. Suppose the mass is displaced an additional 6cm in the…

A:

Q: 1. Find the coordinates of the focus, the equation of the directrix, and the length of LR for each…

A: Note: As per the Bartleby guidelines, we cannot author handwritten solutions, so we are authoring…

Q: 7. Police plan to enforce speed limits by using radar traps at 4 different locations within the city…

A: The probabilities of two events having separate probabilities P(a) and P(b), the probability of the…

Q: Write out the first four terms of the Maclaurin series of f (x) if  f (0) = 2, f'(0) = 3, f" (0) =…

A: We have to write the first four terms of the Maclaurin series of f (x) if f0=2, f'0=3, f''0=4 and…

Q: Express the following statement in "if...then" form. Then write the statement's converse, inverse,…

A:

Q: 3. Determine tautology, contradiction or contingency a. -p→ (q→ r) and q→ (pvr) b. (pvq)^(pvr) →…

A:

Q: Part I. Calculation: Find the solution of each Differential Equations. 1. sin x siny dx + cos x cos…

A:

Q: A city has a population of 260,000 people. Suppose that each year the population grows by 5.75%.…

A:

Q: Determine whether the series n Σ. (+)" n=0 converges or diverges. If it converges, find its sum.

A:

Q: Convert the number from octal to binary form. 725 eight 725 eight = two

A:

Q: Please carefully find the domain of the function f(x, y, z) = as a familiar surface. 4x²+92²-25y and…

A:

Q: Round your answers to the nearest thousandth. 230e0.35 = e-0.9 =

A: Introduction: A crucial constant that appears frequently and serves as the foundation for natural…

Q: Let G = (a, b | a² = b² = (ab)?). a. Express b²abab³ in the form b'a'. b. Express b'abab³a in the…

A: Given: The expression is G=a,b|a2=b2=(ab)2. To Express: (a) The expression b2abab3 in the form of…

Q: a. Use the Colley method to come up with a rating for each team, then rank them. b. What were some…

A:

Q: Find the circulation and flux of the field F = -x²i-y²j around and across the closed semicircular…

A:

Q: Consider the following Gauss-Jordan reduction: 1 0 -656 0 1 Find E= 0 -6 0 1 07 5 6 0 1 | E = = 0 0…

A:

Q: Solve the given initial-value problem. dy dx y(x) = = x + 7y, y(0) = 2 Give the largest interval I…

A: Sol:- dydx=x+7yA first order linear ODE has the form of y'x+pxy=qxSubstitute dydx with y' y' =x+7yy'…

Q: Solve the following differential equations. y' = d. 4. xy² + 2 = (3 — x²y)y', y(-1) = 8. 7

A:

Q: Let's create a matrix that reflects around a line that is perpendicular to the vector n = [0.375,…

A:

Q: 5. Consider the sets: A = {m € Z/m = 6k+9 for some k € Z} B = {m € Z/m = 3w for some w€ Z} Is ACB?…

A: Given that A=m∈Z|m=6k+9 for some k∈Z and B=m∈Z|m=3w for some w∈Z. Let x∈A Therefore, x=6k+9 for some…

Q: 1. Find the value of the Euler phi-function for each of the following integers a) 100 b) 256 c) 1001…

A: Euler Phi-Function: Let n>1 be an integer and the prime factorization is n=p1k1·p2k2···pnkn, then…

Q: A rancher has 120 yards of fence with which to enclose three sides of a rectangular field (the…

A:

Q: Driving down a​ mountain, Bob Dean finds that he descends 4600 feet in elevation by the time he is…

A: Given, Bob Dean descends 4600 feet in elevation by the time he is 4.4 miles​ (horizontally) away…

Q: The given family of functions is the general solution of the differential equation on the indicated…

A:

Q: Show that the power series (a)-(c) have the same radius of con- vergence. Then show that (a)…

A: A series is represented as ∑n=1∞ anx-cn where an's are the coefficients of the  series for n=1, 2, ……

Q: Suppose T is a transformation from R² to R². Find the matrix A that induces T' if T is: a) rotation…

A: First we take anticlockwise rotation matrix of 2x2  then according to gives value we change theta…

Q: 2. (D² + 2D + 1)y= 1 (ex-1)² ANSWER: y = e(C₁+C₂x-In/1-e *1)

A:

Q: How does the subfield lattice of GF(230) compare with the subfieldlattice of GF(330)?

A: Consider the theorem "For each divisor m of n, GFpn, there exists a unique sub-field of order…

Q: Given the below matrix, determine the following. Show all work. a. The eigenvalues for the matrix.…

A: The given matrix is A=4-162162-18 (a) The characteristic equation of the matrix A is given by…

Q: Express the following statement in "if...then" form. Then write the statement's converse, inverse,…

A: The given statement is "No dirt is sufficient for no cleaning". The "if...then" form of the given…

Q: Solve the following differential equations. y' = dy dx ㅠ cos(x)y' + sin(x)y = 2cos³(x) sin(x) — 1,…

A:

Q: 3. Prove that if a is an . odd number and b is an integer then b² a² +9.

A:

Q: 10. What is the join and meet of the following matrices? ^-6 1 A and --[i J B = 이

A:

Q: Yihan recently learned the asymptotical analysis. The key idea is to evaluate the growth of a…

A: given functions g1: 3ng2:n!g3 : n2+ng4 : n3g5 : log2n g6 : logn2g7 : logn!g8 : 2n+1g9 : ln ln ng10 :…

Q: Plz answer all parts

A: Formula:

Q: Compute the curl of the vector field F = -4zi - 5y 3-4x k. =url= =

A: Given,  The Vector Field,F→=-4zi-5yj-4xk The Curl of the vector field is to be calculated.

Q: Place the following functions in an asymptotically increasing order. n log(n!) nn < V 1000000 2n…

A: Given that nlogn!nn10000002nlogn2nn!2nlogn2+100nn5+n210nn

Q: How did you get (0 + 2 - 1 - 2t) in the subtraction part?

A:

Q: Q8. Consider the following basis sets M and N 3 HUD 2 3 M = and N = -3 ∙1 5 Can the orthonormal…

A:

Q: Differentiate the Maclaurin series for 1/(1 − x) twice to find the Maclaurin series of 1/(1 − x)^3.

A: We have to differentiate the Maclaurin series for 11−x twice to find the Maclaurin series of 11−x3.…

Q: Prove that, for every positive integer n, there are infinitely manypolynomials of degree n in Z[x]…

A: To prove: there are infinitely many polynomials of degree n in Zx that are irreducile for every…

Q: Given the below function and graph, determine the following. a. A Fourier series representation of…

A:

Q: dx (f+g)' -f'+g' (5)-95-19 24. Find the derivative of the function F(x) = in two ways: by using the…

A: Differentiation of the function

Q: Let f(x, y, z) = In (2-√√x² + y²). (z- (a) Evaluate f(3, -4, 9). (b) Find the domain of f. (Enter…

A: First we evaluate f(3,-4,9)  for this we put x=3,y=-4and z=9  values in given function  In 2nd part…

Q: Let E be the splitting field of f (x) = x pn - x over Zp. Show that theset of zeros of f (x) in E is…

A: Given E be the splitting field of fx=xpn−x over Zp. We have to show that set of zeros of fx in E is…

Q: Q--4: a) Let R be the relation on the set A = {1, 2, 3, 4} defined by aRb if and only if 2ab + 1.…

A:

Q: pose f:R Z, where f(x) = [2x-1]. If A = {x:1 ≤ x ≤ 4}, find f(A). If B = {3, 4, 5, 6, 7}, find f(B).…

A:

Q: Alonzo wants to buy a bond that will mature to $5000 in seven years. How much should he pay for the…

A:

Q: 1. Use the (a) Gauss-Seidel method until the percent relative error falls below &s = 5%, 10x₁ +…

A: Let x1 be x, x2 be y and x3 be z. Total Equations are 310x+2y-z=27-3x-6y+2z=-61.5x+y+5z=-21.5From…

Q: Assume that a rocket is in space and is following the path y = – 6(x − 7)² + 3, from left to right…

A: