Determine the equation of a rational function with vertical asymptotes at x = - horizontal asymptote of y = and x-intercepts of 3 and y-intercepts of-. (T-4 marks) 2"

Q: 3. If p + q = 6 & pq = 3, where p > q- a. Find the value of (p – q) b. Find the value of p³ – q³ – 5…

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Q: B. FOURIER SERIES OF PERIODIC FUNCTIONS 4. Interval 0 <x<n, function, f(x) = sin 2x. %3D

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Q: Q16: What's mean by a nilpotent element of a ring R? Find all nilpotent elements of Zg-

A: Nilpotent element of a ring

Q: 6. Evaluate * y" + 9y = 0; y(0) = 2 , y'(0) = 9 2cos3t + 3sin3t 2cos3t + 9sin3t C. A. 3(cos3t +…

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Q: Example S = {q1 = 2 + x + 4x², q2 = 1 - x + 3x², q3 = 3 + 2x + 5x²} a. Show that S is the basis for…

A: The given question is related with linear algebra. Given that,               S = q1 = 2 + x + 4x2 ,…

Q: e" + 3x 08. lim, e' + 0.5x ,2

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Q: PROBLEM 8: Find the general solution to ty" + 3ty – 3y = t²e*, t > 0

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Q: 3. Check for monotonicity for the following functions. TR = -20² + 14Q %3D TC = 20 + 10 100 AC = Q +…

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Q: 1-Find the area of the region R under y=x? + 3x +2 Between x-1 and x-2 2-the region bounded by…

A: To find the volume of the resulting solid, when the region bounded by y=1x, the x-axis x=2 and x=3…

Q: Q26: Define the integral domain ring. Is every ring an integral domain?

A: Definition of integral domain:- A nonzero commutative ring in which the product of any two nonzero…

Q: 011: Explain the relationship between ideal and subring.

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Q: (2) Express the vector ū = < 3, 2 ,7) as a sum of a vector parallel to DC ond a vector perpendicular…

A: Consider the points A-2, 3, 1 , B0, 0, 2and C-1, 5, -2. We have to solve the following :…

Q: 24: Define ring. Is every subset of a ring R also a ring? a a ilnotent elen

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Q: لتكالتحلم ملبهلعللمو) محلمولوفحلكرللت )هلهد x^ )5-x = )ه ,4 %3D

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Q: plve for the unknown values using Decomposition Methods

A: We have to solve the linear system of equation using decomposition method.

Q: Q12: Define the concept of field. Is Z a field?

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Q: f(t) = [1– uzm(t)](2 sin t – sin 2t) | |

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Q: 1. Let g : D →R be a function on D and (c, ) C D for some c € R. Then lim g(x) = 1 (l E R) if and…

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Q: Question 8 A bag contains 1 blue marbles, 7 orange marbles, and 22 green marbles. Someone offers to…

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Q: e" (1-e*) (1+x)[In(1– x)] 12. lim, 0

A: Introduction: In mathematics, limits are the factors at which a feature tactics the output for the…

Q: Q4) Solve the boundary value problem y 3y + 2y 0 with %3B y'(1) = 1 , y(3) = 2e* – e? h = 0.5 %3D

A: Given data differential equation y"-3y'+2y=0 with y'(1)=1    &amp;   y(3)=2e4-e2     and h=0.5…

Q: Determine whether each of these functions are invertible. If it is, find its inverse. a. f:R → R…

A: The function is said to be invertible if the function is one-one and onto The function is one-one if…

Q: Find the general solution of the following differential equation. dx - 18 - 40x=t dt The solution of…

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Q: Q6: Let R=(Z,+, .). Find a) Characteristic of R b) Prime ideals of R c) Nilpotent elements of R d)…

A: a) Characteristic of ring: a positive integer n is said to be characteristic of ring R if for any…

Q: A herd of American buffalo (bison) can be modeled by a stage matrix similar to that for the spotted…

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Q: (e) By carefully drawing tangents to the curves shown, estimate f'(0) for each of the functions…

A: Solution:-

Q: Q7: Define the cancelation law. Is it satisfy in any ring?

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Q: + 2d = 6 – 2c + 3d :+ 2d + 10d =

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Q: 7. Evaluate y" + y' = t; y(0) = 1 , y'(0) = -2

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Q: Question 8 Given AABC shown in the graph beloW, if it is the case that: AXYZ=T{3,1}\Rx - axis…

A: From the triangle ABC The vertices of triangle ABC is A (-1,-1) B(1,2) C(-2,4)

Q: Use the extended Euclidean algorithm to find the greatest common divisor of the given numbers and…

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Q: Q3: What are the definitions of pointwise and uniform convergences? Compare between them in example.

A: Solution:-

Q: union of a collectionm of connected sets that have a point in common is conne

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Q: THE LAPLACE TRANSFORM For Numbers 1 and 2. Find the Laplace transform of the following functions…

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Q: – one function from X into

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Q: te Use an appropriate substitution to solve 2yy+ r? + y? +x =0.

A: The solution is given as

Q: Define f, g: R → R as if f(x) ={3x – 2 if -13 and g(x) = 8x – 1. Find f o g and gof. %3D

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Q: example for (integral domain ring, divisor). Q13: Define and give an zero

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Q: {: 2s-3 "hat is L- { equal to? s2-12s+13

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Q: 15. (a) Find the quadratic approximation for the function f(x) = x3/2 centered at a = 4. (b) Use…

A: 15a Given function is fx=x32. We have to find the quadratic approximation for the given function…

Q: 26: Define the integral domain ring. Is every ring integral domain? an

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Q: 4) Among the following equations, the only differential equatiom degree is: dy = 5x + 3 dx A) d'y dy…

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Q: U(at) = U ( 5,t)-0 Hiws Solve Utt = 16 Uxx %3D K= 4 U t CX10) = o 2 uCX, o) = X (5-X ニ

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Q: Q4 prove that 1. Let R be a commutative ring with identity and I be a maximal ideal of R. Then the…

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Q: Exercise 14 Let G be a group. Which of the following statement(s) is/are true: I. If G is noncyclic,…

A: Given G is a group. (I)  if G is non - cyclic , then there exist a proper non - cyclic subgroup of G…

Q: Find the demand function for the marginal revenue function. Recall that if no items are sold, the…

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Q: Find the solution to the following system of equations using the Gauss-Seidel method 12x1 + 3x2 –…

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Q: For Problems 4 – 6, compute the indicated power. 4. (-v6 + iv2)* 5. [vZ (cos + isin ) +i sin- 6. (-…

A: #4 and #5 evaluating by polar form, and #6 is solve by Cartesian

Q: 1. Solve for the element 4-2 of the inverse of matrix A below. 8 -1 A = 2 1 6 3 1 2 4 1

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Q: Qi: (A) Let R =(Z12, +12-12). 1. Find all maximal ideals of R. 2. Evaluate char. (R). 3. Is R a…

A: Given ring  is    R = ( Z12,+12, .12) (.)  Maximal Ideal :  An ideal  M ( ≠ R ) of        a  ring  R…