1/ For any. topological space (X, T), if T has only three elements then (X, T) is connected.
Q: Given that z, -[3,0.7], 2₂ [2, 1.2] and z, -[4,-0.5], (a) find z, xz₂ and 2₁ x 23 (b) show that [1,…
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A: This is a question from optimization and real-valued function.
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Q: ・ Rephrase the initial value problems as integral equations yzyte, yco) 21 2 * x²= t-2² (0)=0 1 2
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Q: tatements represents this cooling process? se the correct statement)
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A: Fourier transform of the function
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Q: pls
A: We solve by LU factorization.
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A: Follow the steps.
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A: consider the sequence 2,5,12,29,70,169,408...... (a) describe the rate of growth of this sequence.…
Q: Why is it necessary to get acquainted with the sigma notation's properties?
A: Yes, it is necessary to get aware of sigma properties . It help mathematics to improve itself.
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Q: 2. Show that the following functions are harmonic, that is, that they satisfy Laplace's equation,…
A: We have to find f(z).
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Q: Example 3: Find the parametric and symmetric equations of the line passing through the point (-3, 5,…
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Q: 12 Compute for the sum. Answer directly. (2 Points) Enter your answer 8 Σ (3-2) j=0
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Q: x^2 + 5x - y = 6; y = 0; x = 3
A: Please see the attachment According to the guidelines we are supposed to do one problem.
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A: Here given function is a single variable function so we can use double derivative test to check the…
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Q: F(s) = = S (s+1)5
A: We find the inverse laplace of F(s)=s/(s+1)5
Q: the smaller region bounded
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Q: Solve for y esec(4y²−6y+14) = 3x + 1
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Q: Q2.) Determine if f(x) is convex, concave, or none of these also state if it attains a max. or a…
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Q: 52 Simplify: [-p ^ (p v q)] → q-
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Q: Solve the differential equation 3y 3y + 1 (sin ¹x)√1-3
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A: To connect connect option from given question.
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A: For a vector function f(x,y,z) Gradient ∇f=fx,fy,fz Gradient vector is also Normal to the surface .…
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A: This is a question of optimization.
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- Let (X, τ) be the topological space A,B⊂X. In this case, show that it is stated in the photo.Prove that topological space E is not homeomorphic to the spaceY = {(x, y) ∈ E^2 : y = ± x} (E represents R equipped with Euclidean distance, E^2 represents R^2 equipped with euclidean distance)the usual metric space defined by d(x,y)= x-y prove the four propertis of metric space
- let (x,t) be a topological space prove that (x,t) is not connected if and only if there exist A,B belongs to t with x= A union B and A intersect B = zeroIs the set S = [0,1] with the discrete metric d separable? Explain.Show that the closed ball Y in a metric space (x,d) is a closed set .Also show that if (x,d) is complete iff and only if (y,d) is complete
- Show that the closed ball Y in a metric space (X,d) is a closed set. Also show that if (X,d) is complete then (Y,d) is completeLet X And Y be two distrecte spaces. Then X is homeomorphic to Y if and only if X and Y are both infinite?Prove that in a metric space (X, d) every closed ball that is a set K(x, r) = {y e X : d(x, y) <= r}, is closed set. Show on an example that closed ball K(x, r) does not have to be equal a closure of an open ball. signs on the image