Q2: (A) Choose the correct answer for each of the following: 1. The cancellation law holds in a. any ring b. a commutative ring 2. The ring of even numbers (Ze, +, .) is a. with identity b. with zero divisor 3. The elements 2 and 4 have multiplicative inverses in the ring a. (Z6, +61-6) b. (Z7, +7,-7) c. (Q,+,.) c. an integral domain ring c. without identity

Q: Let X and Y be topological spaces and let f : X → Y be a function. Prove that the following…

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A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 4. Consider the function Check whether f is concave, convex or neither. f(x, y) = x² - y² + 2xy + 2x…

A: Please find attachment for the details solution

Q: Question (2): Let f,g: R R = R- 0 be any continuous functions. are they homotopic?

A: Two continuous function f and g from X to Y are said to be Homotopic if there exists a continuous…

Q: Example 10.2. Find the value of y for x = 0.1 by Picard's method, given dy y-x dx (P.T. y + x³y(0) =…

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Q: The difference equation given Ayt = ayt-B can be written as

A: This is the question of generating function, difference equation, counting and finite math.

Q: K be a field extension of a fi is algebric over F if and only of 5 that [56)

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Q: 3. Find the maximum and minimum values of z-a 1 āz on |z| ≤ 1 (where a with la| < 1 is fixed)

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Q: Evaluate the integral ſ sin x dx by the method of geometry.

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Q: 7. Determine the period of each function: a) y sin- n²,7 x b) y = cos 2(x-45") c) y = cos(x +90°)…

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Q: Example 10.23. Given dx = 1.979, evaluate y(1.4) by Adams-Bashforth method. = x²(1 + y) and y(1) =…

A: Problem is solved using Adams-Bashforth Method.

Q: M O 82 63 R

A: Given figure as, Here, MQ and NR are diameters and the indicated measure as arc PQ=?

Q: • Create a symmetric equation of a line with the digits 6, 8 and 4. Does the point D (7,-1,8) lie on…

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Q: 3. Let f [2,3] → {1,3} be a continuous function such that the equation f(x) - x = 0 has a solution a…

A: 3 Give that f:2,3→1,3 be a continuous function such that the equation fx-x=0 has a solution x in…

Q: Find solutions which satisfy initial conditions: 13. y' + y = 0, y(0) = 1, y'(0) = 0; 14. y" - y =…

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Q: n 18. Let H be a subgroup of all automorphisms of a field K. Then the fixed field d of K.

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Q: Let D be the portion of z = 2x + 5y inside z2 + y² = 1, oriented up, and let F = (y, z, -z). Compute…

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Q: 1.4 Compute the value of ₂ (sin x − log x+.e* ) dx using Simpson's th rule. 8 0.2

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Q: 2. x=9-y², y-axis; about x = 9

A: Given that region is bounded byx=9-y2⇒x =(3-y)(3+y) and y-axis ; revolving about x =9

Q: 9) If f(z)=u- iv is analytic in the z-plane, then the C-R equations satisfied by it's real and…

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Q: Q2: Use the shell method to find the volumes of the solids generated by revolving the regions about…

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Q: 2) f(x)dx= 0.5 by using Simpson's rule with h = 0.5 then b= A 15 B2 CI D 2.5

A: Option c is correct

Q: {(x,y): y=e}; {(x,y):y2e²}; (x,y): xy ≥ 1, x>0, y > 0.

A: This is a question from a real-valued function.

Q: 2. Let AM₁ (R) be given. (a) If AA=0, prove that A-0₁. Does this hold if A € M₁(C)? (b) Suppose that…

A: This is the problem of Linear Algebra and Linear Transformation.

Q: (B) Find all maximal ideals of (Z8, +8,8).

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Q: 6. Check the convergence of the following series: (a) Σ (1+; )" 8 tan-¹n (b) 1+ n² 1/n (0) Σ…

A: For a convergent series, the general term always converges to zero as n approaches infinity. If the…

Q: Determine ¹ 4s²-5s +6 (s+1)(s² + 4)

A: To find the inverse Laplace transform of the below function. L−14s2−5s+6s+1s2+4

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Q: 1 A=-1 -1 1 1 1 det A =

A: The following steps are used to obtain the solution. Enter the matrix A at the MATLAB prompt ≫. Use…

Q: 3x+4y-2z+ cos6x+9 exp(x)=-9 5x+2y+z=-3 x-y+5z=-11

A: Note:- This system contains some trigonometric terms. so, we'll use graphical method for solution.…

Q: consider the following: u = , v = (a) Find the projection of u onto v. (b) Find the vector…

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Q: Let K be an extension of a field F and let f(x) € F[x] be a polynomial of degree n≥2. Then a€K is a…

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Q: 1. D² {Sin ² x 3 2. JD²-15² √2e²x3

A: Here D is the differential operator. D=d/dx

Q: The sum of the series Σ n² - n + 1 n! - is

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Q: 3. Find the maximum and minimum values of |-| on |z| ≤ 1 (where a with lal < 1 is fixed) 1

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Q: 1. Mr. De Mesa put up a business that offers computer repair which he charges a base of P 350.00 for…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 10) Which of the following statements is false? a) fR is reflexive, then RnRep b) ROR' p R is…

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Q: Find D (x") where m, n E N. Distinguish between the cases where m>n; m = n; and m<n,

A: To distinguish between the given cases :-

Q: Use your learning on exponential functions to answer the following: 1. You take out Php 20,000 loan…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If S and T are normal linear operators satisfying ST* = T* S and TS* = S*T, show that their sum S+T…

A: I have used just definition of normal operator

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Q: The temperature, 7 °C, in an office is controlled. For a particular weekday, the temperature at time…

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Q: 3) Using mathematical induction, show that for all integers P(n): n ≥ 8, n can be written as a sum…

A: We have to show that for all integers Pn, n≥8, n can be written as a sum of 3'sor a sum of 5's or a…

Q: Using (a) Jacobi Iterative Method and (b) Gauss-Seidel Method, obtain the solution [12x₂ + 3x₂ −5x₂…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: b 8 b) Explain (in words) how you could find the number of paths between vertex a and vertex e which…

A: As per the question we are given a undirected graph with seven vertices a, b, c, d, e, f, g And we…

Q: 7. Determine the period of each function: a) y sin- b) y = cos 2(x-45°) c) y = cost = cos(x+90°)…

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Q: Let X and Y be two topological spaces. X is connected and Y is disconnected are they homotopy…

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Q: 7. Determine the period of each function: a) y sin- x 2r 7 b) y = cos 2(x-45°) c) y = cos(x+90°)…

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Q: Thinking-OPTIONAL-Do you want me to mark this question? 7. If f(x) = mx²-x+2 and g(x)=3x² +nx-4, and…

A: A quadratic function of the form fx=ax2+bx+c  represents a parabola. Here, a, b and c are the…

Q: Let S be the solid of integration of the given integral Q. (1.) Sketch S and label its boundaries.…

A: Given,Q =∫02∫-4-y20∫x2+y28-x2-y2ydzdxdy 0≤y≤2 ,-4-y2 ≤x≤0 ,and x2+y2≤z≤8-x2-y2