Suppose that X and Y are topological spaces and f: X- Y. Show that f is continuous iff for each closed set C CY, f-'(C) is closed a closed subset of X.

Q: (1 2 3 4 O = (3 ).r = G 2 3 4 5 6) 5) 1 4 5 6 2 2 4 1 3 6 1 3 4 5 5 2 4 3 1 6 Find the orbit of 1…

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Q: . Let R be the ring of all complex numbers and R' the a b b a ring of all 2 x 2 matrices of the form…

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Q: Fit an exponential curve of the form y = ab* to the followin 1 3 4 6. 1.0 1.2 1.8 2.5 3.6 4.7

A: Introduction: The graphical method has the disadvantage that the straight line drawn may not be…

Q: Raul has a wall 4 units long and 2 units wide in the Cartesian plane centered on the origin. this…

A: In this question, the concept of the graph is applied. Graph The graph of a function is the…

Q: using mathematical definition of z transform derive  [rn sinw0n]u[n]    = [rsinw0]z-1…

A: Given,x[n]=rnsin(w0n) u[n]To find: Z-transform of x[n]

Q: (2 0 2 Consider the matrix A = 0 2 1. Find a Jordan matrix J and an 1 -2 0, invertible matrix Q such…

A: The Jordan form of the matrix is given by finding the eigenvalues of matrix A. Then we find the…

Q: 1 Given that L-(4+9)) = 8in(Bt) – sin(Dt) L-'(+4)(s²+9) Match the following values. 10 is the value…

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Q: Solve using Gaussian Elimination with back-substitution or Gauss Jordan I - 3y + 2z = 18 %3D 5x -…

A: Since there are two equations and 3 unknown i.e. 2 Rows and 4 columns but For the method to solve…

Q: Q2: Find a root of x- 0.5 – 2-2x = 0 by using Newton-Raphson method correct %3D 4 decimals so that…

A: Given: f(x)=x-0.5-2-2x To find: Root of a given function by using Newton-Raphson method correct to 4…

Q: Consider the surface S given by the graph of z = x sin y on the domain D = {(x,y) |0 < x < 3,0 < y…

A: There are two parameters for surface parametrization

Q: 3" + 27+1 (c) Evaluate 5" n=1

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Q: The size of an unborn fetus of a certain species depends on its age. Data for Head circumference (H)…

A: Given that H = -30.98 + 1.822t2-0.9193t2log(t). Where t is age in week.

Q: 13 Practice TANGENT PROPERTIES pri L AB is Solve for x. 3. Both segments are tangent to the circle.…

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Q: Find the work done by F over the curve in the direction of increasing t. F = -7y i + 7x j + 9z 7 k;…

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Q: x2 – 2x – 8 lim - 21. = 6

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Q: 4 a Evaluate In 3. b On the axes below, sketch the graph of y = Inx -3 2 3 -2 -3 The graph y = In x…

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Q: Evaluate the work done between point 1 and point 2 for the conservative field F. F = 6x i + 6y j +…

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Q: 1 Find the L-1 s(s²+2s+5) Oetsec 2t e-tcsc 2t 으글e-tsin 2t et cos 2t

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Q: dz IV. Suppose z is a function of æ and y, and a? – y? = 2"e®y. Solve for dx

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Q: Hamiltonian cets / path in Bipartite graphe Show that the following graph G is bipartite by…

A: Given a graph. First we have to show that the given graph G is bipartite by partitioning the…

Q: Compute the left regular representation of the group G = {e,a, b} given by the group table below by…

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Q: You spin the spinner, flip a coin, then spin the spinner again. Find the probability of the compound…

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Q: Determine whether the Fourier series of the following functions converges uniformly or not. Sketch…

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Q: . Use the Euler , improved Euler and Runge-kulta. methools to solve the fellowing ODES: d. ý <…

A: We can solve this by using given information

Q: 1 point) Let f(x)dx = 3 and "(f(x))*dx = 13. Find the following integrals: S. cf(z)dz = v)*dx – (J,…

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Q: Express the vector - 14i + 8j - 8k as a product of its length and direction. - 14i + 8j- 8k =TOi+…

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Q: School fees at a certain school are due at the beginning of the year. The fees are set at R12000 for…

A: Solution :-

Q: Exercise 1.9 Suppose z = a + bi, w = c + di. Define z < w if a < c, and also if a = c but b < d.…

A: Suppose z=a+ a+bi and 2 = c+d2 are distinct complex numbers either If a not equaal to c then either…

Q: Use Euler's method to a) compute y(1), where y(x) is the solution of the initial value problem: dy *…

A: As per policy, we are allowed to answer only 1 question at a time. So, I am answering the first…

Q: f If f(x, y) = y cos(x) – x³ In(y), find the second partial derivative dy dx

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Q: Fine th Lanrent seviesad 9. 1-24 1-22 - Zo= 1 -

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Q: Consider the curve C on the yz-plane with equation y? – z + 2 = 0 (a) Sketch a portion of the right…

A: (a) The curve C on the yz-plane is given as follows: y2-z+2=0 The graph of the given curve is as…

Q: Let U={a,b,c,d,e,f.g,h,k}, A={a,b,c,g}, B={d,e,f,g}, C={a,c,f} and D={f,h,k} 1. Compute: a.) A U B…

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Q: Consider the group D4 = (a, b) = {e = (1), a, a², a³, b, ab, a²b, a³b} %3D %3D where a = (1 2 3 4)…

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Q: Solve using Gaussian Elimination with back-substitution or Gauss Jordan -リーz=0 a + 2y - z = 6 2x ー=5…

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Q: 3 If X 1 - the value'of X" is 1 3n - 4n (a) 2 + n 5-n (b) - n | 3" (- 4)" (c) (d) None of these 1"…

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Q: 4 a Evaluate In 3. b On the axes below, sketch the graph of y = Inx 3 2 -2 =3 The graph y = In x is…

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Q: Solve the initial value problem (3+x*)y" + 4y = 0, y(0) = 0, y(0) = 12. If the solution is y = co +…

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Q: Q1) Solve

A: We solve given PDE by direct integration method.

Q: If f is.q field a hom- saplar monic polphomial in tay can be factored as q, product of monie primes…

A: Any non-zero non-unit element as a product of primes up to order and up to units. Now  If a≠0 and…

Q: II. Consider the function g defined by 1 g(r, y) = cos (T2 T) + log3 (2 – y) Do as indicated. . In…

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Q: Answer the following using Jacobi Method. Show complete solutions. The iteration should have atleast…

A: The Given equations are: 9x1 - 13x2 + 4x3 = 111 4x1 + 22x2 -13x3 = -128 8x1 + 8x2 + 17x3 = 10   To…

Q: 1. Prove that if f(x) is bounded and measurable on E, and c is any constant, OMNIA then S, [f(x) +…

A: Given, f(x) is bounded and measurable on ETo prove: ∫Ef(x)+c=∫Ef(x) dx+c m(E)

Q: Question Ris the region bounded by the functions f(x) = 3 sin (x) + 2 and g(x) = 6x + 2. Find the…

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Q: The linear equations -3x-y = 3 and 6x + 2y = 1 is said to be %3D O inconsistent O independent…

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Q: Q4) The state space representation of a dynamical system is given as: *(t) = [ ) x(t) + [LLO %3D…

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Q: |Suppose that dy = y3 + y? – 9y – 9 dx %3D and that the point (13, –2) lies on the graph of (x, y).…

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Q: If a function f: D R is differentiable at a point (a, b)ED, then f is continuous at (a, b);

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Q: Let G = 3xy²a, + 2za, Given an initial point P(2, 1, 1) and a final point Q(4, 3, 1), find ſ G•dL…

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Q: Consider the group D4

A: Given: Group D4=a,b=e=1,a,a2,a3,b,ab,a2b,a3b and a=1 2 3 4, b= 2, 4 To find : The value of…