1) a) Evaluate the limit. 1 1 lim 3 x x+3 x-3

Q: : Find the divergence of the vector field At the point (2,4,1). F(x, y, z) = x² √yi+j+zk

A: We have to find the divergence of the vector field F(x, y, z)=x2y i^ +yxj^+zk^ at the point (2, 4,…

Q: Find the inverse, if it exists, of the following matrix using row of operations. First, find the…

A: oiWe find Inverse of matrix by guass Jordan elimination method.  Steps for Gauss-Jordan Elimination…

Q: Every ring without zero divisor it is an integral domain. T OF O *

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Q: 4. Consider a3(x)y"" + a2(x)y" + a₁(x)y' = 0 (a) What's one trivial solution? (b) Suppose the…

A: Please see the attachment

Q: A sales person makes a base salary of $400 per week plus 12% commission on sales. (a) Write a linear…

A: Salary person makes a base salary of $400 per week plus 12 % commission on sales. Lets say he makes…

Q: Determine if the graph is Hamiltonian or Eulerian. If the graph is Hamiltonian, find a Hamilton…

A: Number of vertices is 5. For every pair of vertices x and y, deg(x)+deg(y) is greater or equal to 5.…

Q: Surface of a sphere is a two-dimensional Riemannian space. Compute the Chrtstoffel symbols.

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Q: -<t <-/ Let f(t) be defined as f(t) = t -<t</ TU TC <t<n Extend f(t) periodically and find the…

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Q: Determine true or false. are linearly independent. True False 1 2 ··· 2 0 -3 The vectors

A: The given statement is                             The vectors 12-3 , 20-1 , 04-5 are linearly…

Q: PC costs the store owner $1000 and a laptop costs him $1500. Each PC is sold for a profit of $ M…

A: We have given conditions..by comparing these conditions we get first three questions answers... And…

Q: Find the residue of 3 Z Z²-1 at z→ ∞

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Q: Let n be a positive integer. Using congruences, show that 3n+3 +23n+3 is divisible by 7.

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Q: Find the half-range sine series for the function f(t)=nt-t², in the interval 0<t<n.

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Q: / Reversing the order of integration fxsinydydx.

A: To find- Reversing the order of integration ∫0π∫0xxsiny dy dx

Q: Jse partial fractions to find the inverse Laplace transformation of the below Determine L−1 { 4s - 5…

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Q: has solutions of the form R(p) etmzting whe

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Q: 30Find the Laurent Series of 3 flz 1: J = C:/Z/=1 (2-1)2 (2-3)

A: We find Laurent series of given function.

Q: Find the standard matrix of the linear transformation T: R² → R³ given by T(x₁, x2) = (2x₁ - 3x2, x₁…

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Q: show that the following function analytic f(z)= 4e²+ Sin Z arp

A: Explanation of the answer is as follows

Q: oes the line segment from (0,0) to (a,0) subtend th

A: The objective is to find at what point on the line y=b does the line segment from (0,0) to (a,0)…

Q: (c) Continuing from part (b), suppose we can find functions and z so that (uoz)(x, y) is an μ…

A: Note: : Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: The particular integral of the difference equation Yn+3 - 6yn+2 + 12Yn+1-8yn = 3h is

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Q: partial differential equation

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Q: 6. Find the Laplace transform of the foll (a) g(t) = et+2+ sint cost+to(t-2 (b) a(t) = te sinh3t.…

A: Introduction:   The Laplace transformation is very significant integral transformation that is used…

Q: Find the half-range sine series for the function f(t) = nt-t², in the interval 0<t<n.

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Q: The graph G₁ has 6 vertices, all of degree 3. How many edges does G₁ have? The graph G₂ has 8…

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Q: R: y = 2x + 1,x+y=7,x=8

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Q: Find the optimal solution to the following problem. Minimize f (x1, X2, X3) = x₁² + 2x2² + 10x3²…

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Q: lid obtained by y the curve y = o x=1 will be:

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Q: ex² =e-5x-4

A: Given equation is ex2 = e-5x-4

Q: The graph G is a planar connected graph. It ha

A: Given, the graph G is a planar connected graph. It has 11 edges, and 7 faces.

Q: What is angle XWZ

A: A round quarter, additionally called a circle quarter or a disc quarter, is a segment of a disc…

Q: Find the divergence of the vector field At the point (2,4,1). F(x, y, z)=x²2√√yi + -j + zk

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Q: In the group G = Z24, let H = (4) and K = (8). (a) State the Third Isomorphism Theorem. (b) List the…

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Q: 2 Express (+) in polar form O 3 [cos 67+isin 67] O 13 [cos 70+isin 70] O 3 [cos 70+isin 70] O 13…

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Q: Let f: A → B be a function with A₁, A₂ ≤ A. Determine if the following statement is true or false.…

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Q: Choose the write answer for L(f'(t)) O Non of These O F(0)+sf(0) O F(0)-sf(0) O SF(0)+f(0) O…

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Q: Consider the linear operator defined by Show that T is compact. E1 E2 E3 T:l² l², x = (1, 2, 3, ...)…

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Q: 3 Z Find the residue of z² - 1 2 Z at z→ ∞00.

A: Use the formula of residue at infinity to solve this problem as in next.

Q: 4. In one of the biggest schools in Metro Manila, 80% of their high school students are known to…

A: Given: Hypergeometric Probability Distribution To find: Solution

Q: 1. What is the largest n such that Pʼn is a subgraph of K4? 2. What is the largest n such that Cn is…

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Q: Construct a nondeterministic FSA that recognizes the language generated by the regular grammar G =…

A: Given: G=V,T,S,P To find: Solution

Q: An office building worth $4 million when it was completed in 2015 is being depreciated linearly over…

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Q: S 00 -² dx = LEN π 2

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Q: Find the angle between the two vectors A = i +j+ k and B = 2i+j-k

A: By using the formula of angle between two vector, we solve the given problem as in next step.

Q: Q.5. If we have two vectors (V₁ and V₂), V₁ is a vector perpendicular on the plane passer through…

A: Introduction: When a vector is along the direction in another vector, the two vectors are parallel…

Q: R: x = 2y-y², y - axis

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Q: :y= x,y = 2x2 − 3x

A: To find centroid we need to find area bounded A between curves  then centroid x =∫abx×fxdxAy…

Q: Let T: R² → R² be the counterclockwise rotation through the angle Then the standard matrix of T is:…

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Q: (0) Let R be a commutative ring with identity and I be ideal of R. Then I is primary if and only if…

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