Question 1 Evaluate the following integrals using residue theorem: (a) x² To (b) 2x³ sin wr Lo (1 +2²)² d (c) COS E L∞ (a² + 1)(x²²+4) dx -dz

Q: Determine if the series is convergent or divergent using Ratio test. Σ 42n+1(n+1) n=1

A: Solution

Q: 1) solve b finite diffrence method Ду4-ху! -2хубов убежнуснен

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Q: Consider y' - 2y = 3e2x with y(0) = 2. Using Runge-Kutta method with h=0.1, find the relative error…

A: The given differential equation is : y'-2y=3e2x with y(0)=2. h=0.1.  To find: Relative Error on…

Q: 6. Let A and B be n x n hermitian matrices. Suppose that A² = Ins B² = In (1) and [A, B]+ = AB +…

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Q: Explain how to solve a trigonometric equation graphically. Paragraph V BI U A V Lato (Recomm... V…

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Q: Q.7: find the directional parametrization of the line segment joining two point A(2,1,3) and…

A: It is a basic questions of 3-D geometry , we have equate the equation only

Q: Determine the value/s of D if the graph of the equation x² + 4y² + Dx - 4y + 2 = 0 a single point;

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Q: When approximating f(x) dx using Romberg integration, R4,4 gives an approximation of order:

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Q: A circle has a diameter of 26 units. What is the area of the circle to the nearest hundredth of a…

A: To find the area of the circle, you will use the formula for finding the area of any circle.…

Q: 2. Find the maximal interval of existence and uniqueness of the solutions to y' = e√1-1²-y², y(0) =…

A: Solution: Given,y'=e1-t2-y2,    y0=0We know that  by existance and uniqueness theorem,The initial…

Q: The centroid of the area bounded by the parabola y^2 = 4ax and the line x = p coincides with the…

A: Please see the attachment

Q: 1000 .Silver Heights Secondary School has a capacity of 1600 students. The school, which is in a…

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Q: By using Laplace transform to solve y" + 4y + 8y = sint with y (0) = 1 and y' (0) = 0, what would be…

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Q: II. Fill in the missing entry in each row: Equation of line m X=0 Y=X 2.) X = 2 Point P (x,y) (-2,3)…

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Q: 3. Consider the vector field F(x, y) = (2xy, x² - sin y). Evaluate [.F. F. ds where is the curve…

A: Using Green's Theorem

Q: Let B=Qn (0, 1) be a subset of R. Consider a function f: N→ B defined by f(n) = an where an nEN. (a)…

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Q: By using Laplace transform to solve y - y = sin(2t) with y (0) = 1, what would the particular…

A: The solution is given as

Q: Let G be a finite group of order 4 containing no element of order 4. Explain why every nonidentity…

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Q: 8. Using the Mean Value Theorem and Rolle's Theorem, show that³+x-1=0 has exactly one real root. 9.…

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Q: Find the Laplace transform of f(t) = t²e7t

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Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler method with h=0.1, y(1.3) = y(A)…

A: Solution:-

Q: 12 Two towers AB and PQ stand on level ground. The angles of elevation of the top of the taller…

A: Given that  ∠KAP=5o ∠QBP=20o Height of the taller tower = 70 meters

Q: Example 9.6 A square of 6 ft sides is to be subdivided into three equal parts by two straight lines…

A: Given figure is  where parallel lines EF and GH divides the square ABCD in three equal parts. Let…

Q: If A and B are bounded subsets of R, then prove that AUB and AB are bounded.

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Q: The demand function for a commodity is given by D(z) = 2000 – 0.1z – 1.01z² Find the consumer…

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Q: Show that for any 1 ≤ k ≤n. T) (1) = n²(n²-1²)...(n² – (k − 1)²) 1.3.5 (2k-1) .

A: We will use the basic knowledge of Chebyshev polynomials to answer this question completely and…

Q: Let a be an arbitrary positive irrational number. Show that the unit circle |z| = 1 is the natural…

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Q: The following data gives an approximation to the integral M= f(x) dx N₁(h) = 1.2341, N₁ ( = 1.0282.…

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Q: x Suppose the slope of the tangent line at any point on a curve is If the x²+4y² curve passes thru…

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Q: GRAPHS 1 2 3 4 5 6 7 8 PATH 5 Edges 2 6 3 7 TRAIL 4 8 Edges WALK Edges

A: Walk: A walk is a sequences of vertices and edges of graph i.e. if we traverse a graph then we get a…

Q: In a psychological experiment investigating how individuals change their assessments of probability…

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Q: Find the Inverse Laplace Transform of 1 s²-8s+25

A: The given function is 1s2-8s+25 completing squares 1s2-8s+25=1s2-8s+16+9=1s2-24s+42+9=1s-42+9

Q: R(t) = Romeo's love/hate for Juliet at time t J(t) = Juliet's love/hate for Romeo at time t What…

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Q: 1 0 5 -2 0 1 4 1 0 0 0 0 Row 1 - x1 + 0x2 + 5x3 = -2 Row 2 - 0x1 + x2 + 4x3 = 1 Row 3 - 0 = 0…

A: Given: System of equations, x1+0x2+5x3=-20x1+x2+4x3=10=0 To find: The solution of given system.

Q: 2. A boat is being pulled into a dock by a rope attached to it and passing through a pulley on the…

A: Solution :-

Q: a Define a relation on by (a,b) ER if and only if - EN. Which of the following properties does R…

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Q: 4. Six different groups of children would like to visit the zoo and feed different animals. (Assume…

A: Given: Six different groups of children would like to visit the zoo and feed different animals.…

Q: a. The input is a day of the week, and the output is the number of students in this class born on…

A: Note:- As per our guidelines, we can answer the first three sub-parts of this problem as exactly…

Q: Question 1: Given the following system of Initial value Problem (IVP) ==-2-3y, 20 = 2(0) = -1 1…

A: We will use the basic knowledge of differential calculus to answer all the parts of this question…

Q: (am,n)m,neN is a sequence with am,n 20. The sequence is for a fixed m in n monotonous increasing and…

A: Given: am,nm,n∈ℕ am,n≥0 for all m,n∈ℕ am,n is monotonous increasing for fixed m and for fixed n.…

Q: x Suppose the slope of the tangent line at any point on a curve is x²+4y² If the curve passes thru…

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Q: Angela currently owes $6,000 to a friend who is charging her interest of 2.80% p.m. She is required…

A: We have to calculate the size of the equal payments using three months as the focal date. Simple…

Q: 2. Consider the function (a) Sketch the curve y f(x). (b) Find the area of the region between the…

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Q: What is the area of the shape?

A: Given,

Q: 5. Suppose that a water tank is shaped like a right circular cone with the tip at the bottom, and…

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Q: Suppose f(x, y, z)=+P-(1.2.3). A. Find the gradient of f V/= 1+ J+ Note: Your answers should be…

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Q: You have a set of N dice, where each die d has m faces numbered 1, ..., m. How many ways are there…

A: Let the function for determining X from n dice be: total (m, n, X) Sum(m, n, X) = Finding Sum (X -…

Q: ܒܢ J nπL s²L²+ n²π²] 22

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Q: Consider xy' = y(lnx-lny) with y(1) = 4. Using Runge-Kutta method with h-0.1, approximate y '(1.3).…

A: option c is correct i.e. (c) -1.92711

Q: Power 2 ·cos. x. ² d.x.. 015 a f. cos

A: Solution a: Given ∫00.5cosx2dx Since we know that cosx=1-x22!+x44!-x66!+... then…