Let X = {1,2,3,4,5} and let T = = {x, Ø, {2,3,4,5}, {1,2,5}, {2,5}, {1}}. O (X,T) is Hausdorff but not connected. O (X,T) is connected but not Hausdorff. O (X,T) is neither connected nor Hausdorff. O (X,T) is connected and Hausdorff.

Q: S. (22² 2. 2 (2x² – 3x) dx

A: ∫25 2x2-3x Apply the Sum Rule:    ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx =∫252x2dx-∫253xdx

Q: Solve for the following quantities given the matrices below. 3 -5 1 L= 0.5 -1 3.5 2 0 4 3j E= 5.5…

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Q: Given F(A, B, C, D) = A'B'C'D' + A'B'C'D + A'BCD' + A'BCD, express F(A,B,C,D) and F '(A,B,C,D) in…

A: Solution: Given that F(A, B, C, D) = A'B'C'D' + A'B'C'D + A'BCD' + A'BCD Now, truth table Row no.…

Q: [3(cos 18° + i sin 18°). [2(cos 20° + i sin 20°)]³.

A: De Moivre's Theorem: cosθ+isinθn=cosnθ+isinnθ where n∈ℤ

Q: 9. (a) Use the method of Lagrange multipliers to determine the minimum and maximu values of f(x, y)…

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Q: Using any of the methods discussed for both numerical differentiation and numerical integration…

A: f( x) = sinx - x3 + 1 By Midpoint method f'(a) = (f(a+h) - f(a-h)) /2h

Q: Use (a) Fixed Point Iteration method (b) Newton-Rhapson method and (c) Secant Method to find the…

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Q: 4. Find the Fourier Series of the given periodic function. 4, f(t) = {_1 -π≤ t ≤0 0 < t < π

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A: We will sketch the region bounded and find boundary curve to use polar co ordinate for volume .

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Q: 4. Let Z5 = {0,1,2,3,4}. 4a) Find the value of x that makes (2+5) X5 4 =_1 in Z5 true. Complete the…

A: Given :  ℤ5 = 0, 1, 2, 3, 4. To find : (i) The value of x in  ℤ5  that satisfies  (2 +5 x) ×5 4 = 1.…

Q: Use (a) bisection method and (b) false position method to find the solution to the following within…

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Q: a) Find the area of R. (b) SET UP a (sum of) definite integral(s) that is equal to the arc length of…

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Q: Use a double integral to find the area of the region. One loop of the rose r = 5 cos(30)

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Q: 29. A body temperature of 50°F is placed outdoor where the temperature is 100°F. If after 5 minutes…

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Q: 18. The graph of 3[H(t2) - H(t-3)] is given by:

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Q: For the function ƒ(x, y) = 4x³ + x² − 7, find the solution of the differential equation from x = 0…

A: We can solve this using mid point method

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Q: Consider P2 (R) together with inner product: Find an orthogonal basis for P2 (R). (p(z),9(2) = Г'р…

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Q: 1 -4 7 1 3 -7 sin30 cos20 -2 = 0

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Q: Find the solution. (D³ + 6D² + 11D + 6)y = 0 -2x Av=ce-tre-te +c -3x By=c₁e*+c₂ C + czte © y =…

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Q: Use multiple equation Newton-Raphson method to determine one of the roots of the following…

A: Given x2+3y2=10x-22+y-12=3

Q: 4-Let (Z12, +12) be a group and let S={4,6}, find subgroup H generated by S. if exist

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Q: c) Using the Euler-Lagrange equation of the Calculus of Variations Optimize (-16y² + 144y + 11yy' −…

A: Given functional is ,                                            I[y(x)]=…

Q: 1. How many corner points are there in this LP problem A. 1 B. 2 C. 3 D. 4   2. Which of the…

A: Introduction: Linear programming is a mathematical technique for optimising operations given…

Q: For the function f(x, y) = −xy2, find the solution from x = 0 to x = 1 with an increment of 0.2 by…

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Q: List the members of these sets, x | x is the square of an integer and x < 100.

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Q: For questions no. 4 and 5. Given: Radium decomposed at a rate proportional to the quality of radium…

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Q: Show that there are no Boolean lattices with cardinality 5.

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Q: Consider the following initial value problem y(1) = 1 y'(t) ye2t; t € [1,6]

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Q: The parabola x² - 2x + 2y + 7 = 0, has a vertex at (1,3). O(-1,3). O (-1,-3). O (1,-3).

A: Suppose the equation of a parabola is of the form  y=ax2+bx+c where a, b and c are constants. The…

Q: [2 + m 3 1. Given A= 1 a. (AB)¹ - A b. |4A-¹ + 2B-¹| a. 2AB-¹ 1 2 -1 -1 4 5+ ml and B = [-1-m 2 91 3…

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Q: Using any of the methods discussed for both numerical differentiation and numerical integration…

A: Solution : Equation is f(x)=ex-cos(x)-2Numerical differentiation method, x0=0 , x2=3 h=0.75 table…

Q: Let Xn, Yn be any two sequences. If XnL, YnM, then Xn YnL M

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Q: The Laplace transform of the function u: [0, ∞) → R [(t-2)² + (t-2) sin(5(t-2)), for t > 2, =…

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Q: i s'ex eo e V². (-^x) dy dz -jz 00

A: Solution : a∧x.a∧x=1 ∫01∫01a∧x∈0e-jz.(-a∧x)dydz =-∈0∫01∫01e-jzdydz =-∈0∫01e-jzdz =-j∈0e-j-1

Q: Determine inverse z-transform of the following equations: 2² b. (2-1)(z-0.5)

A: Solution

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A: Let F be a field. Here , f(x) ∈ Fx. Here , First we assume that , f(x) is maximal ideal in Fx. We…

Q: d²y 5. Consider the differential equation dy 6- +9y = 9x + 3. dx dx² (a) Find the general solution.…

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Q: 7.Find xy of z = 2x³-5xy²

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Q: 1. Evaluate the definite integrals using (a) integration, (b) trapezoidal rule, (c) the mid-ordinate…

A: Here we have to evaluate a Integration  :  ∫2612x-1dx                             ⇒12∫2612x-1dx…

Q: Write the statement in symbolic form: "BBM and Sara Duterte may have won the election but Leni and…

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Q: a. Find the Fourier transform of the given function. 2A f(t) == t + A, 75150 2A f(t) = osts/ f(t) =…

A: This is a problem of Fourier expansion.

Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. 5. Lim xsinx x→ 0+ 5

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Q: List all the ordered pairs in the relation R = {(a, b) | a divides b} on the set {1, 2, 3, 4, 5, 6}

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Q: (b) Use the GaussJordan function to solve the system: 1 2 3 4 5 6x₁ 91 1-325-4 6x₂ 37 6 1-2 4 35 63…

A: Augmented matrix of the given system 123456911-325-463761-24356332-1456814-2-1365695-6-34-21-4

Q: ƒ(x) = 3x4 +√4x; ƒ"(1.2) 6

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Q: d²y (a) Solve the differential equation +y dx² y'(0) = 0. got up (4) pap = sin(x) + cos(x) with y(0)…

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Q: Please provide a step-by-step and clear solution to each of the problems below. 1) Parabolic…

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