1) (i) Prove that every sequence converges to every point in a space with the trivial topology. (ii) Prove that no sequence converges to any point in a space with the discrete topology.

Q: Q2/Using inverses to solve the equations: 4x1 + 5x2 + X3 = 2 X1 - 2x2 - 3x3 =7 3x1- X2 - 2x3 =1

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Q: b) - a +b-c+d = 0 – 2a + b+c-3d = 0 a + 2b - 3c + d = 0 2a + 3b +4c- d 0

A: Let us considre the system of matrix Ax=b Using Cramer's rule, the solution of the system of…

Q: Find the convolution of the two functions: f(t) = 2t and g(t) = () Cos 3 t. %3D

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Q: Let the curve C be traced by the vector-valued function Rt) = cos(rt) i + xt j + sin(rt) k. %3D

A: The vector valued functions are usually represented in the form: r→(t)=x(t)i^+y(t)j^+z(t)k^, where…

Q: The length of the major axis of an ellipse with foci at (-1, 2) and (3, 2) that passes through the…

A: Here we use basic defnition of major axis

Q: dy Differentiate parametrically to find dx in terms of t: %3t2, y3 6t

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Q: 그 n=1

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Q: If money is worth 10%, m=4, find the number of deferred period (d) of a deferred annuity with a…

A: Given , m= 4 Time = 2.5 years.

Q: a) Use logarithmic regression to find a logarithmic function that best fits this data. Round each…

A: Given: The data below: To find: a) The logarithmic function that fits the given data using…

Q: If R =[E , F] ,Q =[F , C], Z = [D , B]. (a) Find the algebraic displacement vectors. (b) Determine…

A: (a) Algebraic displacement vector for points x1,y1 and x2,y2 can be written as follows:

Q: -Zくtく-! -1< く ぐく2 3). fa) = 24

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Q: 2. Consider the system -2x + y -2y and its corresponding direction field. (a) Skotch a number of…

A: Introduction: Slope fields (also known as direction fields) are a graphical depiction of the…

Q: The numerical value of e1 will be ....

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Q: Q4/ Solve the differential equation b) = v1+ sinx(1+ y?) when y(0)=1 dx

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Q: A jet flies 250 km from Ottawa to Toronto at a rate of v + 50. On the return flight, the plane…

A: To calculate the difference in the flight times of the initial and return flights.

Q: 2 Determine the domain and range of the function y = Vx* + 10x + 24.

A: Domain is the values of x for which this function exist. Range is set of all the values that can…

Q: show that whe ther RERiemman L-,1} yot

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Q: (ii) =I+ 2y (iv)

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Q: Find the first derivative at x 2 for the function given by the data 1.0 1.5 2.0 3.0 0.4057 0.69315…

A: By the finite difference method      f'(x) ≈ {f(x+h) - f(x-h)}/2h                         [Second…

Q: Determine whether the series tan converges.

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Q: Let N, (h) be the approximation of f'(xo) with some numerical differentiation scheme depending on h.…

A: Use the following Richardson's extrapolation formula, to obtain the best approximate value.…

Q: 2a +b-c+d = 1 За - 2b + 2с-3d %3D2 2a - b+c- 3d = 4 5а +b-с+ 2d %3D-1

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Q: 1. If the region bounded by the two curves is revolved about x = 4, what is the volume of the…

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Q: 2. An observer views a space shuttle from a distance 2 miles from the launch pad. (a) Sketch a…

A: Use trigonometric identity of tan(theta) to solve the question. Tan(theta)=Perpendicular/Base

Q: Let n = pq where p and q are two distinct primes and consider Zn. Further, let [a] E Zn be an…

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Q: 7. Find the indicated partial sum for the indicated terms. a. 4+16+64+256 + ... 10 terms b. 30+…

A: Introduction: A series is the sum of the terms in a sequence, rather than a list of terms like a…

Q: Let f be a function that admits continuous second partial derivatives such that VS(7, y) = (4r" –…

A: Given that, A function of continuous second derivatives , such that ∇fx,y=4x3-2a2x+2a2y,…

Q: Find all equilibrium points for the following system of equations: dr 10z (1 - 6) – 20zy dt dy = -5y…

A: This is a problem of the system of the differential equations.

Q: Find the Eigenvalue and Eigenvector 2 2 1 A = 2 2 1 5 -1 1

A: Note: Eigenvalues of a square matrix A is given by roots of the characteristic equation det(A -…

Q: 2. Let R = {(x, y) : x,y E R}. Prove or disprove that R is reflexive, symmetric and/or transitive if…

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Q: Consider the recursive sequence a =(@+5) with a, =3. If 1<a,<5 then n+1 O A. The sequence (a ] is…

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Q: Let K be the splitting field of – 5 over Q. - • (a) Show that K = Q(V5,i/3) • (b) Explicitly…

A: Hi! For the part (c), we will be needing the information that what all groups we have seen before…

Q: (ii) = 0.3r - 3ry dt = -2y + 0.1zy dt

A: Note: As you asked only Question2 (ii) part so, I answered here only part (ii).

Q: c) Evaluate the integral: 2z drdydz where the solid S is defined as: S = {(x,y, 2) € R* : 2Vz²? + y?…

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Q: -2 -4 7 [x1' 8 | -9 10 -6 12 X2 -12||X3 -11] [X4] -4 9. 9. -5 8. -12 -8 [-3] I|

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Q: Find the Singular Value Decomposition for the matrix A 1 A = 1 Recall Singular Value Decomposition…

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Q: QUESTION 10 A classroom of children are asked to indicate which Power Ranger is their favorite. The…

A: Frequency is defined as number of times something is observed.  Using this defination of frequency…

Q: %3D when

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Q: A second-order non-homogeneous differential equation is given by d2y/dx2 − 10 dy/dx + 21? = 21x2 +…

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Q: Let n e N with n > 2 and let G, = (V, E) be the graph with vertex set V = {v1, v2, . . . , v2n} and…

A: Since you have posted a question with multiple subparts, we will solve the first three subparts…

Q: Q4/ Solve the differential equation a) xy. = 1+x + y+ xy dx

A: Solve the differential equation, by Variables separable method

Q: Find the first derivative at x=2 for the function given by the data 1.0 1.5 2.0 3.0 0.4057 0.69315…

A: By finite difference formula     f'(x) ≈ {f(x+h) - f(x-h)}/2h                  [second order…

Q: Express EC by combinations of the vectors a, b and 7.

A: We have to write EC vector in terms of a,b and c

Q: 1. For the following exponential function identify the initial value, the growth factor, and growth…

A: The exponential growth or decay can be represented by the following equation. fx=abx Where a is the…

Q: Q.1/ Find the area of the region bounded by the line y = 1 – x and the curve x = 3 – y?.

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Q: Complete the following table of values of a function p : {3,4,..., 11, 12} {-4, -3, ...,4,5} 3 5 10…

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Q: The amount A of dollars accumulated after t vears through an investment of Ag dollars at an interest…

A: To find the doubling time for an investment made at the following interest rate: (A) 7% interest…

Q: 7. Find a third degree polynomial function with zeros 3,-4, and

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Q: 39. If the scale factor of two similar solids is 5:13, what is the ratio of their corresponding…

A: We use properties of similar solids.

Q: Suppose you wish to approximate the area under thế grupli The area is sketched below. a) Divide the…

A: a) The graph of fx=ex2 is given on the interval -1≤x≤1, that is, -1, 1. If the interval is…