RULE: 1. Write your student number clearly. 2. a= 7th digit of your student number 3. b= 8th digit of your student number 4: c= Remainder of a+b according to modulus 3. b) Use proper test to investigate the convergence of the improper integral e-(e+1)x x(+2) - (c+1) -dx.

Q: 11. If cu and u+v are in H, c is scalar, and u,v are in H; then a. H is a subspace of vector space…

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Q: Problem # 1 Use the method of disks/rings to determine the volume of the solid obtained by rotating…

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Q: Q. Now make a multiplication table for modulo 3. ol 1 2 IN 0 1 2

A: Since you have uploaded multiple questions according to our guidelines we have solved first question…

Q: Find the volume V of the solid obtained by rotating the region bounded y = x², x = y²; about y = 1 V…

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Q: Find the exact value that Ise conclude that the series diverges. n=2 n+2 n +3 converges

A: We have the series ∑n=2∞1n+2-1n+3

Q: If A = 2 4-2 0 0 2 3 -2 4 0 3 then find det (A) BY HAND using a cofactor expansion of your choice. 1…

A: Given: The matrix A is given by:  A=12-244-20320143023 To find: We have to find the determinant of…

Q: Use the guidelines of this section to sketch the curve. 7 - 16 HHH # -6

A: Let the given function has asymptote at X= 4 and x= -4 We can draw a graph as below.

Q: If A is an ideal of a ring R and 1 belongs to A, prove that A = R.

A: Given: A is an ideal of a ring R and 1∈A.To prove: A=R

Q: O a Ob 1. Which of the following is a set of linearly independent vectors? a. (1,2,1),(1,2,2),…

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Q: 3. Find all of the equation. (a) y'= -x (c) (e) = x ln x y" = 2xe* ==cos x (i) y7e4x y'= -x sin x x…

A: Solution:

Q: B 5. Which of the following is not a basis for R²? a. (1,2),(3,8) b. (2,2),(3,2) c. (2,3),(4,6) d.…

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Q: Please type out your solution so that it may be able to be read by me so that they are easy for me…

A: d(t) = 3t2+8t  Differentiating of the above equation with respect to t , we get Velocity, v(t)…

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Q: Find an arc length parametrization r₁(s) of r(t) = (et sin(t), eª cos (t), 5eª) . Assume t(s) = 0…

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Q: 10. Find the solution to the IVP d²u dt² +9u=t, u(0) = 0, -(0)=0. du dt

A: Answer

Q: Question 2 Given is f(3) = 10, f '(3) =6, f "(3) =7, and that all other higher order derivatives of…

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Q: 2 -2 -[:]~-~-[;) - - [³ ]-~^»-[*³] and and e₂= and Y₂ = 5 6 Let e, = into y₂. Find the images of The…

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Q: 7 If A = then find all real eigenvalues and corresponding eigenvectors.

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Q: x = c1 cos t + c2 sin t is a two-parameter family of solutions of the second-order DE xn + x = 0.…

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Q: Q5: A) Solve: The system of differential equations.: dx =-y+t dt dy dt x-t B) Solve: y" + 3y' + 2y =…

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Q: 2. x+y≤10 x+2y≤16 x20;y 20 P = 0.5x + y +Y र X

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Q: 22 2 b) Find S, the sum of series=+=+ 3 15 35 c) Hence, find Sas n→∞. ·+...+ 2 4n²-1 in terms of n.

A: (b)The given series is: 23+215+235+ . . . +24n2-1. We have to find the sum of the series, Sn. (c) To…

Q: linear 1-1 transformation then T(),...,T(V) are also linearly independent. (Explain why the 1-1-…

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Q: Given f(x) = 2x²-5x - 1 and g(x) = 2sin x, determine the values of x when f(g(x)) = 2 for 0 ≤ x ≤ 2.

A: The composite function is defined as a function made of the other functions, where the output of one…

Q: A thermometer is removed from a room where the temperature is 70° F and is taken outside, where the…

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Q: Find an explicit solution of the given initial-value problem. dy y2 – 1 y(3) = 3 dx 1 = y-1 y +1 -문…

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Q: Consider the Lotka-Volterra predator-prey model defined by dx dt dy dt = -0.1x + 0.02ху = 0.2y…

A: We have to find period of each population by using the graphs.

Q: Verify Green's Theorem by evaluating both integrals I rax+x2oy= (х от са JJ L: y2 dx + x2 dy dA Әх…

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Q: Find the equation the circle that runs through the points

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Q: Differentiate the function G(s) = Answer 38² 7es + s G'(s) =

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Q: 1. (a) Find the eigenvalues of ((2A¹)-¹), given that A = -[29]. (b) A is an n x n skew-symmetric…

A: (1) (a) We have to find the eigenvalues of ((2AT)-1)2 for given matrix A.  (b) A is an n x n…

Q: Write the solution set of the given homogeneous system in parametric vector form. 2x₁ + 2x₂ + 4x3 =…

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Q: 3. 5. 7. dy 21 dr 1+12y=3 11. In Exercises 7-12, solve the given initial-value problem. dy dt +2,…

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A: Given differential equation dydx=yxy5-1dydx=xy6-ydydx+y=xy6divided by y6  on both sides…

Q: Find the divergence of the vector field F. F(x, y) = 5x²i + 3y²j

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Q: 13. For the IVP y' = t - 1, y(1) = 0, use Euler's method with a step size of 0.5 to approximate…

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Q: 2. Tangent lines to parabolas Consider the parabola y=x². Write an equation of the line tangent to…

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Q: Approximate the area under the curve graphed below from x = 1 to x = 7 using right endpoint…

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Q: For the function f shown, graph f(x+1)+3. NOTE: Use the controls below to transform the graph.…

A: Graph of the function is given, we have to sketch the graph of the function fx+1+3.

Q: 9 Suppose that a finite group I acts smoothly on a compact manifold M and that the action is free,…

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Q: 2. Find the linear DE that produces the null and particular solutions Yn (t) = Cet and yp(t) =…

A: Since general solution of DE is sum of null solution and particular solution. So first find the…

Q: Let R be the region between circles x² + y² = 36 and x² + y² = 1. Sketch the region and evaluate the…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Maclurin Series Expansion in obtain the of the following functions. a.) f(0) = ws 0 b.) f(0) = sin @…

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Q: Solve the given differential equation by separation of variables. xy + 5x - y -5 xy - 2x + 6y - 12…

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Q: Let u, v, w be three non-zero vectors |v| +6|u| +5 u+V+W w+u|-|u+w |u|v is a positive real number is…

A: |v| and |u|  are  non negetive real number so |v|+6|u|+ is positive real number    u ,v ,w are three…