Evaluate the following: z²+2 a. S12=1 (2²-9)(z²+16) dz b. Jclz=2 zdz

Q: 2. Let (X, A, μ) be a measure space. If {E} CA and E₁ E₂ E3 C..., then prove that H(UE) = lim (En).

A: Let X,A,μ be a measure space. Let {En}n=1∞⊂A and E1⊆E2⊆....then, To prove: μ∪n=1∞En=limn→∞μ(En).

Q: 2. Let p,q and r be the propositions p: Grizzly bears have been seen in the area. q: Hiking is safe…

A: Given- Let p, q and r be the propositions  p: Grizzly bears have been seen in the area. q: Hiking is…

Q: 11. Show that the quotients field of the integral domain Z[i] = { a+ib: a, b e Z} is K={x+iy: x, ye…

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Q: Q.1B) Prove that: I = ₂ Cos(x) dxdy sin (1) 2 where R the region bounded by x + y = 1, x = 0, y = 0

A: Given that  I=∫∫RCosx-yx+ydxdy Where R the region bounded by x+y=1, x=0, y=0

Q: $. 12-1 (2²+-)(2-2) 1-4z+6z² 1 -dz .d

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: E 11 D 12 14- 10 17 16 C B

A: For a connected graph, the vertex is where two or more edges meet. The degree of a vertex is the…

Q: 2π -233 In A4BC, LA= 1 and AB. AC = 4. The length of angle bisector of ZA is: (B) 2 (C) 3 2 (D) 2

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Q: 1 - 27 S e+ix - x) w dw

A: As per the question we have to solve the integral from -∞ to ∞ And we will use Fourier transform and…

Q: 3. Determine whether the following integrals are convergent or divergent, and evaluate those that…

A: We know that , Improper integral of the function fx over interval -∞ , ∞ are of the forms ,  ∫a∞…

Q: In the isosceles triangle ABC, AB=AC=5 units and BC=6 units. Find the location of the point D on the…

A: Consider the information given in the question and draw the diagram, Here we can observe that ABC…

Q: Discuss the merits of integral error compensation and compare it with derivative compensation

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Q: True or False The Actual time between January 20,2009 to September 14, 2009 is 234 days

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Q: Given a periodic function # S(x)=√Q, TT, Q=0 Q=x² π, T -A < X <-- 2 T 2 <x< f(x+2π) The following…

A: Explanation of the answer is as follows

Q: Let F(x) = f(x5) and G(x) = (ƒ(x))5 . You also know that a¹ = 14, ƒ(a) = 3, ƒ'(a) = 8, ƒ' (a³) = 6…

A: Use the following formulae, to obtain the solution. Chain rule for differentiation:…

Q: 10 dx 64-Г 3

A: It is known that  ∫0π2sinpt cosqdt=Γp+12Γq+122Γp+q+22. Here, Γx is the Gamma function.

Q: thanks

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Q: (2xy¹e³ + 2xy³ + y) dx + (x²y²e³ − x²y² − 3x)dy = 0

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Q: Find the volume of the following gure. If needed, round to the nearest hundredth. * **** 297,024 ft…

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Q: Question Which of the following is a potential function f for F(x, y, z) = (2x cos(yz). -x²z sin(yz)…

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Q: An object in rectilinear motion moves with velocity v. The table shows u (in meters per second) for…

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Q: M. -5z + 11 2² - 10z + 21 Iz 61 2 dz Use any of the results in this $ (a) -12ni (b) |z| = 9 33 Book…

A: We have to solve the given problem.

Q: Problem 2. To prepare for summer, Diffy E. Kew is trying out a new lemonade recipe. Through rigorous…

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Q: 8. Find the directional derivative off at the p in the direction of v = () of f(x, y, z)=x²exx, p =…

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Q: η Σ (1) 5 k=1 k odd = 6" - (-4)" 2

A: Here we prove that ∑k=1k oddnnk5k=6n--4n2

Q: Given dy² c cos x + D sin x Cxe-* +4-5y = 2e*, the correct y, is (solve) Option 2 O Ce-x Cex Option…

A: given problem is  d2xdy2+4dydx-5y=2e-x clearly there is misprint in the first term it should be…

Q: Find a particular solution to the differential equation using the Method of Undetermined…

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Q: (a) Prove that any subgroup of Sn contain either even permutations only or equal number of even and…

A: As per guidelines we are allowed to solved one question at a time so i am solving first one please…

Q: A tank contains 240 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

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Q: Let C be the curve y = 12 11 10 9 8 7 6 5 4 15 x³ 1 + 4 3x 25 Find the arc length of C shown above.…

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Q: Construct a graph with vertices P, Q, R, S, T, U that has an Euler circuit and the degree of T is 4.…

A: We know that, Euler Circuit:  A circuit that uses every edge exactly once is called Euler Circuit.

Q: se Newton's method to approximate all the intersection points of the following pair of curves. Some…

A: The equation in the form y=f(x) represents a curve in the xy plane. The point of intersection of the…

Q: How many sets of 3/4 are in 2 1/2

A: Find how may sets of 34 are in 212. There are three circles given and two and half of the circle is…

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Q: The intervals on which f(x) = x² In x is increasing and decreasing, and intervals of concavity and…

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Q: 9. Evaluate the integral, where C is the above half of the circle = R from z₁ = 1 to z₂ = -1.

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Q: 8. Consider the complex function f(z) = x² + y² + 2ixy. a) Show that f'(31) does not exist. b) Show…

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Q: Put the following program in standard matrix form: Z = X₁ + X₂ X1+ 5x2 <5 2x₁ + x₂ ≤ 4 maximize:…

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Q: The area in the first quadrant, bounded by the curve y = 2x1/2, the y-axis and the line y – 6 = 0 is…

A: The centroid of volume of solid revolution about the line y=k is obtained by the following formula.…

Q: Given a periodic function -x, -L<x<0 { f(x)= x, 0<x<L f(x+4) Therefore L = 4.

A: Given function is fx = -x, -L&lt;x&lt;0   x,   0&lt;x&lt;Lfx+4

Q: Letr = (15462 37) and q = (2 4 5 6) be permutations in S7, written in cycle notation. What is the…

A: The given permutations are r=(1 5 4 6 2 3 7) , q=(2 4 5 6). To write: The second line of r in…

Q: The matrix A 250 = 300 TTO -2 21 -2 1 one of the eigen vector is (solve) 11 Option 4 O 3 園 in Option…

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Q: (a) Use the Midpoint Rule with n = 6 to approximate integral 8 x-6 S6 dx x+8 Write your answer exact…

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Q: 3. Consider the Initial value problem ry' = y + r ln(r); y(1) = 2 (a) Estimate y(1.5) using Euler's…

A: To solve given differential equation using Euler's method and RK-4 (classical) method. y'=yx+ln(x),…

Q: Are the following statements true or false? 1. There exist vectors u, v, w R³ such that u V, V-W, W…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: What is the correct periodic function represent the given graph -21T -2x+2π, -<x<0 0<x< f(x)={-n,…

A: GIVEN GRAPH equation of line passing through x1, y1 &amp; x2, y2 is f(x)=y1+y2-y1x2-x1(x-x1)

Q: construct a graph with vertices Q,R,S,T,U,V,W that has an Euler path and the degree of U is 1 and…

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Q: Suppose H is an inner |(x,y)| ≤ 11x11-1111 product space. Show Ужуєн.

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Q: Q.6: Use power series to solve the differential equation; Y y" + xy + y = 0

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Q: Simplify 12 05 7 5 5 = (mod 5)

A: Introduction: The modulus operator, which operates between two accessible operands, is an addition…

Q: Solve using Gauss-Jordan elimination. = 14 = 12 2x13x25x3 x₁ - 4x₂ Write the system of equations as…

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