4).   Use the Ratio Test to determine whether  ∞ n = 1 an  converges, where  an  is given. State if the ratio test is inconclusive. ∞ n = 1 34n(n!)4 (4n)! Identify  an.     Evaluate the following limit.   lim  n → ∞  an+1 an       Since  lim  n → ∞  an+1 an   1,   . please show step by step .

Q: A right circular cone is inscribed in a sphere. 16 in. The radius of the sphere has a length of 16…

A: Given that diameter and slant height are equal,

Q: Lercise 8.13. (a) Is S₁ ≈ Z4 U(7)? Justify your answer. Is S4 Z6 U(5)? Justify your answer.

A:

Q: QI) A- Find asymptotes for the following functions: x²+2x² (1) (3) B. IF f(x)=√√4-x, g(x)=x², Find :…

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

Q: Let V and V' be vector spaces over a field F and let f: V→ V' be a linear map. Which of the…

A:

Q: It is given that a sequence of Newton iterates converge to a root r of the function f(x). Further,…

A: We are given fx=x-r2gx So, f'x=x-r2g'x+2x-rgx

Q: 3. Let S be the subset of Mmn containing all matrices A such that (A)11 = 0. Determine whether or…

A: Introduction: A subspace is first of all a non-empty subset of a vector space. If it is a vector…

Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

A: Let W be subspace spanned by u's. Here , u1 = 1101 , u2 = -131-2 , u3 = -1011 Also , y = 644-1 We…

Q: Calculate the flux of the vector field F = (xy, xy, z) through the surface > Σ = {(x, y, z) = R³ : z…

A: Given That : F=(x y , x y ,z) ∑=(x,y,z)∈R3:z=1-x2-y2,z≥0 To find : calculate the flux of vector…

Q: Question 4: C 5²-4 a. e2s + (5²+4)² 45 b. e2s+. (s²+4)2 45 c. e-2s + (s²+4)² d. None of the above…

A:

Q: Sketch the graph of the equation and label its intercepts. 7y+x=7 Identify the intercepts of the…

A: Given the equation 7y+x=7

Q: Number of voters 1st choice 2nd choice 3rd choice 4th choice 5th choice 506 Points for candidate A:…

A: In this question, the concept of Baroda Count is applied. Baroda Count Points are assigned to…

Q: Let f (x, y, z) = g (v x² - 4y2² +2² V x² +16y² + 2², where 9 is some nonnegative function of one…

A: Given: Let us consider the given data, fx,y,z=gx2-4y2+z2×x2+16y2+z2 The surface S is given as,…

Q: 16) Consider the nonhomogeneous linear recurrence relation a=2a,-1+2º. an = n2" is a particular…

A:

Q: Find the eccentricity e and distance d from the pole to the directrix. I dentify the cenic and…

A:

Q: Find the derivative of y with respect to the given independent variable. dy dx 5 y = log 16 ex-log…

A: Given y = log16ex - log4x5

Q: (c) Find the remainder of 9045142161 on division by 247 using Euler's Theorem. [Hint: 247 = 13 x…

A: Euler's Theorem: It states that if gcd(a,n) = 1, then aϕ(n) ≡ 1 (mod n), where ϕ(n) is the Euler's…

Q: f(t) = u(t− 3)(t - 3)e-4t

A: In this question, the concept of Fourier Transform is applied. Fourier Transform The Fourier…

Q: Solve the following initial value problem to find y(2). dy 2 at =yt ²-l·ly, y(0)=1 using midpoint…

A:

Q: Find the inverse of the matrix (if it exists). (If an answer does not exist, enter DNE.) 20 -6 -6 -3…

A: To Find: The inverse of the matrix(if it exists).  20-6-6-311-312

Q: Find the limit of the sequence πρὖ + 4 πρ4 +5 c3 - 2e { where - e CER+ and n " cn+1 - ne 0 for any…

A:

Q: 3. Find the maximum/minimum value of y = 2x² + 7x - 10 and where it occurs using partial factoring.

A: Given function is y=2x2+7x-10 we can write it as y=x(2x+7)-10

Q: Can someone add explanation along with the answer. Question: Find the Lagrange's interpolating…

A: We have to find the Lagrange's interpolation polynomial of degree two to find the approximation of…

Q: H.w1: +2y+y=e', y(0)=1, dy(0)=2, find by Euler's method y(0.75). Use a step dt dt d'y dt² size of h…

A:

Q: T a(x¹ B) ax

A:

Q: 1. Let S be the triangular region in R³ with vertices at (2,0,0), (0,6,0), and (0,0,3) with upward…

A: 1 Given S be the triangular region in R3 with vertices at 2,0,0, 0,6,0 and 0,0,3 with upward…

Q: Consider the Initial Value Problem: X₁ x2 = x2 (a) Find the eigenvalues and eigenvectors for the…

A:

Q: Determine whether the matrix is in row-echelon form. If it is, determine whether it is also in…

A:

Q: Which of the following vectors is an element of the subspace W=span{(1,1,0),(0,1,1)}? (a) (2,0,-2)…

A:

Q: 1. 2022 ash Coff ege! X 8x Solf OJN M into the curve y = mege 202 curve f(x) is in the direction by…

A:

Q: Using these sets, find the following: DU (EU F) D = {b, a, c, k} E = {t, a, s, k) F = (b, a, t, h).

A: Given, D=b,a,c,kE=t,a,s,kF=b,a,t,h D∪E∪F is to be determined.

Q: 1. y 125 mm 125 mm 200 mm 200 mm 150 mm 60 mm Determine the coordinates of the centroid of the…

A:

Q: (a) Find a formula for the general term an of the sequence 8 3 4 4' 9 - } assuming that the pattern…

A:

Q: 4. The following independent spinners were spun simultaneously. What are the odds in favor of…

A:

Q: Exercise 8.8. Let p be a prime. Prove that ZpZp has exactly p+1 subgroups of order p.

A:

Q: Consider the following points. (2, 4), (3, 6), (5, 10) (a) Determine the polynomial function of…

A:

Q: 9. Prove that nullity(A) = nullity(AT) if and only if A is a square matrix.

A: Introduction: The nullity of a matrix is the number of linearly independent vectors in the null…

Q: 9. Prove that nullity(A) = nullity (AT) if and only if A is a square matrix.

A:

Q: Given: n(A) = 14, n(B) = 22, n(A n B) = 6 Find n(A U B) O 36 O 42 022 O 20 O None of these

A:

Q: Consider the differential equation (x³ - 4x) y" + 2021xy - 1999y = 0 (a) Find all singular points of…

A:

Q: x1 + x2 + x3 = 2 20x1 + 2x2 - x3 = 25 2x1 + 13x2 - 2x3 = 30 Linear algebraic equation set x1 (0)…

A: Given x1+x2+x3=220x1+2x2-x3=25  2x1+13x2-2x3=30 and x10=x20=x30=0

Q: Show directly from definitions that if f(x) and g(x) are real func- tions, bounded on [0,1], and so…

A: Given: fx and gx are real functions, bounded on [0, 1], and limx→0+fx=2 and limx→0+gx=3 We have to…

Q: Determine whether the set S spans R³. If the set does not span R3, then give a geometric description…

A: I have given the answer in the next step. Hope you understand that

Q: 8 Given the series (-1)" un, such that lim un n→∞0 TRUE? n=1 O The series converges to a finite sum.…

A: Given series is  S = ∑n=1∞(-1)nun Such thatlimn→∞un=0

Q: Let F= (x, y², z²). (a.) Let E be bounded below by xy-plane and above by the sphere x² + y² + 2² =…

A: Given: Let us consider the given, F=x2,y2,z2 Let's determine a) The flux of F through ∂E direct…

Q: Find the maximum/minimum value of y = 10-4x - 3x² and where it occurs using completing the square.

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

Q: The surfaces p = 3 and 5, p = 100° and 130°, and z = 3 and 4.5 identify a closed surface. (a) Find…

A: As per company guidelines we are allowed to solve maximum three sub-parts so i am solving first…

Q: H.w2: Use Runge-Kutta Method with (h = 0.1) to solve the eqaution y" + 3xy' -6y = 0 with y (0) = 1,…

A: The Runge-Kutta methods are a series of numerical methods for solving differential equations and…

Q: (b) To determine To compute: The differential equaiton + x = sin 4t with initial condition x (1₁) =…

A: Given differential equation is: d2xdt2+x=sin4t . . . (1)The initial condition is: xt1=0 And…

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) 9- xy lim (x, y) (1, 2) x² +…

A:

Q: 4. Find the sum of the following series: n=1 1 (a+n)(a+n+ 1)(a +n + 2) (a-n, n = N).

A: Introduction: The sequence of partial sums is very significant in determining the sum of an infinite…