a) Determine all primitive roots mod 61 using course notes,

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Q: a²u ²u + G(x) for 0<x<a, 0 <y<b дх2 дуг If u(x, 0) = 0, u(x, b) = 0 for o < x < a u(0, y) = f(y),…

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Q: lim e²+2t²+ t-0 -k = t-4 Enter your answer in i, j, k form.

A: The given limit is .We have to find the given limit.

Q: = 5₁° ne-*sin2xdx

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Q: Find the 7-base representation of rational number 1 36

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A: Given that: The vertices of a digraph with vertices can have its vertices numbered from  such that…

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A: Given thatHereWe have to write the augmented matrix for this problem.also determine the number of…

Q: 4) Find the solution of initial value problem Utt-4uzz = 0, ∞0 u (x,0) = x cos²x, u₁(x,0) =…

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Q: 1² +2²+...+ n² = n(n+1)(2n+1) for 6

A: We are given expression

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A: Reflexivity:Symmetric:

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Q: 17 D 24 14 18- B pply the nearest neighbor algorithm to the graph above starting at vertex A. Give…

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Q: x + 2 x+5-x + 5 (a) lim Calculate the following limits, or explain why they diverge.

A: Given :

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Q: -2 or (2,5m) or (2,-3) 2 1 T -2 (2.) (0,4) 2 X <= Many Ways to write a point Plot the points whose…

A: To Plot: The given points,To Convert: The given points into rectangular coordinate:

Q: How many six-digit numbers with a possible leading zero, but no repeated numbers are there if the…

A: To find that how many six-digit numbers with a possible leading zero, but no repeated numbers are…

Q: y" + 2xy + y = 1 y(0) = 1, y(1) = 2 Which of the following statement(s)is/are TRUE for the given…

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A: Definition:

Q: Use Legendre to solve this question. Exp(-6y(x-2)-3+2y'(x-2)-²-) = -4(x-1) + x²

A: Given equation is…

Q: 1) Find the general solution of the equation Uzy + Uz Jesent 2€²x+y

A: Solution:

Q: Let G = (V, E) and G' = (V', E') be simple graphs. We say that a graph G is homomorphic to a graph…

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Q: For the curve defined by F(t) = (e-t, 3t, e*) find the unit tangent vector, unit normal vector,…

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Q: Let the sequence 9n be recursively defined by go = 0, 91 = 1, 9n = In-1 +29n-2 for n ≥ 2. Show that…

A: Given recurrence relation:

Q: EXAMPLE 5 Find the center of mass of a solid of constant density that is bounded by the parabolic…

A: We only check the remaining equation. Rest of the parts are true.

Q: Give the Dedekind cut for 35. Your answer should not refer directly to any irrational numbers.

A: To explain the Dedekind cut for ³√5 without directly referring to any irrational numbers, we can…

Q: 3. Construct the natural cubic spline for the following data. f(x) b. X a. C. 8.3 8.6 X -0.5 -0.25 0…

A: Given data:

Q: 4. Prove that, if f : A → B has an inverse, then f is bijective. (The converse is also true, and…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Sketch the region of integration and evaluate the integral. 1 S S 4yª exy dx dy 00

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Q: Blanca would like to purchase a simple retirement annuity that would pay her $400$400 at the end of…

A: Blanca would like to purchase a simple retirement annuity that would pay her at the end of each…

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Q: State and prove the two versions of fundamental theorem of calculus. Discuss the significance of…

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Q: What is the largest positive constant K such that if 0 <r < K, then A. 9 B. 8 C. 4 D. 1 E. 2 ∞r¹²…

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Q: a 14 D 15 10- B Apply the sorted edges algorithm to the graph above. Find the total cost of the…

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Q: a) Alice has asked you to help her classify these functions based on their asymptotic growth rate.…

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A: The given curves are and .The curves intersect at the origin.To find the angle of intersection.

Q: 1) A. Write the elements of dihedral group D with respect x and y. Is D, a p-group? Justify your…

A: A group is called a p-group if it has an order P^n for some prime P.

Q: If the Laplace transform of the function f(t) is F(s), then what is the inverse laplace transform of…

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Q: give the intervals of concavity of f(x)=e^(x²-1).

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Q: Give the Dedekind cut for 1/√2. Your answer should not refer directly to any irrational numbers.

A: Dedekind's cut is a concept in real number theory, introduced by Richard Dedekind, to rigorously…

Q: Consider the vector field F(x, y) = (2x +3+3y)i + (cos(y) + 3x + 2 * 2y)j and the path P that starts…

A: Given:

Q: The graph of a cosine function has an amplitude of 3, a vertical shift of 1, and a period of 4.…

A: The graph of a cosine function has an amplitude of , a vertical shift of , and a period of . These…

Q: In Family B, the middle child is 5 years older than the youngest child.

A: Given that,In Family B, the middle child is  years older than the youngest child.We have to write…

Q: Suppose that p and q are integers with 0 < p, 0 <p+q, and the greatest common divisor of p and q is…

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Q: Explain why the function is differentiable at the given point. f(x, y) = xбe⁄, (1, 0) and fy(x, y) =…

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Q: Calculate the integral SJ xy dx dy x+ D x²7x² 0<x< 1 and o<y<√7_x²} over the domain D= {x,y)ER?

A: We have to evaluate  over the domain  x=y is a straight line passing throwgh origin and  This is a…

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y=x^6,…

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Q: Given 3x^2 +6y^2-z^2 = 36. Find and sketch each of the traces.  what is the quadric surface is…

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