1) Let A be the family of everywhere-defined real functions f so that lim f(x) = 0. x →∞ Decide whether A is an algebra of functions. Show that your answer is correct.

Q: y" + 4y = 28/4 y(0) = 1/2, y'(0) = 0

A: Let Y(s) be the laplace transform of…

Q: Find the surface area of that part of the plane 4x+10y + z = 9 that lies inside the elliptic…

A: We have to find the surface area of the part of the plane  that lies inside the elliptic cylinder

Q: Hence, or otherwise, show that the solution of d²y dx² dy dx is 2 sinh t y = 2 sin sin (…

A: Given that                          where Now, the Euler-Lagrange   equation   is   given by   We…

Q: In a company with 50 employees, the average monthly salary is $5,000. If 15% of the employees…

A: first calculate the total monthly salary for all employees in the company:Total Monthly Salary =…

Q: (ii) 42 = 6(mod 10) 437 = 42(18)+1 (mod 10) = (4²) 18 x 4 (mod 10) = 618 x 4 (mod 10) = 6 x 4 (mod…

A: The objective of the question is to find the remainder when 437 is divided by 10 using the concept…

Q: Give an example of a group G and subgroup H ≤ G such that ♬ is not normal in G.

A:

Q: 4) Create a Venn diagram to illustrate A U (C' U B)

A:

Q: 11. a) Simplify: log b) log√k + log (√k)³ + log²³√k² c) 1 log5 4 + 2 log5 3

A:

Q: 1. Express 3-² == in logarithmic form.

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: When a ball is thrown, the horizontal distance travelled, d, in metres, can be modelled by the…

A: Given that,When a ball is thrown, the horizontal distance traveled, d , in meters, can be modelled…

Q: Linearize 8.12 about dt 2 ot/A x = J + 2 ds + co5x = 0 dt

A:

Q: Suppose that 122x²48x+c=0 for some integer constant c, has a rational root of the form x = (assume…

A: Suppose that for some integer constant c, has a rational root of the form  ( assume that the…

Q: 4. Explain the general behavior of solutions to differential equations of the form: a) df(t)/dt = +t…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: A pension fund has a liability of £65000 to be paid precisely in 4 years time. It wants to…

A:

Q: I bought a new gas lawn mower the other day. This new mower mows faster than the old electric…

A: The objective of this question is to calculate the time saved by using a new gas lawn mower compared…

Q: Previous Problem List Next ‚ Let F = (6x²y + 2y³ + 7e²)i + (5ex² +54x) j. Consider the line integral…

A: Given, and consider the line integral of  around the circle of radius , centered at the origin and…

Q: 1) Let A(x) = -1 0 1 0 -2 -2 -1 x 0 xER. (i) For what values of x is A(z) diagonalizable? Give a…

A:

Q: Given the following table: 0,0 1 X f(x) 0,1 7 0,2 3 Calculate the integral using the Simpson method:…

A:

Q: Example 29 Suppose a set contains the plays "Much Ado About Nothing", "MacBeth", and "A Midsummer's…

A:

Q: One hundred fifty people were surveyed and asked if they believed in UFOs, ghosts, and Bigfoot. 44…

A:

Q: 1. For the function f(x)= -5x² approximate the slope of the tangent line at (-1,-5) using the secant…

A:

Q: Let G = U56 and define two subgroups H₁ and H₂ of G by := H₁ := Calculate H₁ H₂|. {1, 5, 9, 13, 25,…

A:

Q: At point B, the slope of the blue curve is (Hint: Calculating the slope, pay extra attention to the…

A: The slope of the blue curve measures the planes rate of desecnt . The unit of measurement for the…

Q: Utility is a type of function that occurs in economics. When a consumer receives x units of a…

A: Formula used : Let A(x) represent rate of change and f be given function then,

Q: Let a 0 for all x = [a, b]. Let A > 0, B > 0 be constants. S[y] = da [* dx f(x)}√/1+ y^², _y(a) =…

A: Given functional is where  is continuously differentiable function on the interval So to get optimum…

Q: Let F = 3x²i+2yzj+ y²k, let C, be the path made up from the 3 line segments from the points (0,0,0)…

A:

Q: Solve the given initial value problem. dx dt | dt = 3x + y - e4t; = 2x + 4y; The solution is x(t) =…

A:

Q: / Given Z1=1+√3i and 51 Z2 = 2 e 6 Find 2 (Z2)² Z1

A:

Q: I bought a new gas lawn mower the other day. This new mower mows faster than the old electric…

A: The objective of this question is to calculate the time saved by using a new gas lawn mower compared…

Q: A travel agency surveyed 280 people asking about their travel plans for the next year. Use the given…

A:

Q: 7. Is there a potential F(x, y) for f(x, y) = (8xy + 3)i+ 4(x² + y)j? If so, find one.

A:

Q: Y" + 4y' + 4y = et t=o t=o

A:

Q: Q3] Find the value of contour Integral if C is the circle |z1| = 1 e²z dz z3z² + 4z - 4 C

A:

Q: a.) Do nontrivial solutions exist for the following equations? 1 0 1 0 1 0 2 2 2 XI X2 | = | 0 X3 0

A:

Q: 17. Given the functions f(x) = sinx and g(x) = -x² + 4, determine the domain of the combined…

A:

Q: 2. Show two ways of solving the following: 3*+2 – 3* = 216

A:

Q: K Determine if the argument is valid or not. Abby goes to the movies or she reads. Abby does not go…

A: We have to determine the given argument is valid or not

Q: Solve the system by finding the reduced row-echelon form of the augmented matrix. x- 5y + 4z 3x -…

A:

Q: (b) 11, €25x<-1 Calculate the Fourier series expansion of the function f(x)=2,-1<x<1 1,15x

A:

Q: Z (z+1)sinz dz where C is: (1) z-i|=1 (2) |z − 1| = 4

A: (.) Given,        (1). (2).  (*)  Cauchy Residue Theorem: If  is a simple connected domain and  is a…

Q: A loan is to be repaid over 30 years, with month-end repayments of 7,000 . If the interest rate is…

A: The loan is to be repaid over  years.Monthly payment: Interest rate:

Q: I bought a new gas lawn mower the other day. This new mower mows faster than the old electric…

A: The objective of this question is to calculate the time saved by using a new gas lawn mower with a…

Q: How to solve the differential equation and draw the phase diagram?

A: The objective of the question is to solve the given system of differential equations and draw the…

Q: Rewrite the following limit as a definite integral and evaluate it. lim 71-00,

A: We have to rewrite the following limit as a definite integral and also we have to evaluate itWe know…

Q: 4. If you are given the graphs of two functions, f(x) and g(x), explain how can you determine the…

A: The objective of the question is to determine the location of a point that would appear as a zero on…

Q: Q9: Find the first 4 terms of the Taylor series of F(x) = ln x at a = 1

A: The Taylor series formula of f(x) at…

Q: F. Given a metric space M with metric d, verify that any ε-ball is an open set.

A: The objective of the question is to prove that any epsilon-ball in a metric space M with metric d is…

Q: 2. Use the graph of the combined function y = 2* — x² to determine an approximate solution to the…

A: We have given graph of we have to find the solution for the inequlity:

Q: Properties of Determinants. In this problem you are asked to prove some of the properties of…

A: Since you have posted multiple subpart question, we will solve the first three subparts for you, as…

Q: Consider a sphere of radius r centered at (0, 0, 0). Express the following sets in set notation.…

A: Note that : Since you have posted a question with multiple sub parts, we will provide the solution…