Verify Stoke's theorem for the vector function, F = x î+ z² î + y? k over the plane surface x+ y +z = 1 lying in the first octant (figure is necessary for the answer of Q2.)

Q: Verify F(1,1; 2; x) = -x¯ln(1 – x) By expanding each function in a power series about x = 0.

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Q: Evaluate using Laplace Transform: tsin3 3t dt e-3t f(t) = 0,

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Q: If the rate of inflation is 3.4% per year, the future price p () (in dollars) of a certain item can…

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Q: ay" + 4y' + cy = 0 Consider the equation solution of the differential equation is of the form and…

A: It is given that the differential equation ay"+4y'+cy=0. The general solution of the differential…

Q: Consider the differential equation: xy" – y' 18y (1) Making the changes of variable x= e', y=…

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Q: 7) Finol the arymptotes to the cunne n chich are parallel. dothe axis)

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Q: f(C) = | Evaluate using Laplace Transform, find a: n* sin(t + a) cos(t + a) 3 dt 8. f (t) = e2t

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Q: Evaluate using Laplace Transform: tcos 3t dt e-4t f(t) =

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Q: Refer to the following matrices. A = [ -1  4           3  -4          3  0 ]       B =  [  2  3…

A: Given ,  A = [ -1 4           3 -4          3 0 ]       B = [ 2 3           3 1          -2 2 ] We…

Q: Consider the differential formula ay" + 4y' + cy 0 and the nonzero real constants a, c, m, and n. If…

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Q: Use a triple integral to find the volume of the region bounded by z = 7x + 4y, z = 5, and the planes…

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Q: Exercise (3-2): find Fourier series on [0,2n] Question Answer (1) f f(x)%=sinx sin x (4) f(x)=cos x…

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Q: Find the Laplace transform of: 1. f(t) = e(-3t) sin(2t) cos(3t) cosh(t)

A: Laplace transferom of the function

Q: Find the inverse transform of the given functions: 4s2-4s+1 1. F(s) = (s3–4s2+s+6)(s²+5) 3s-6 5s 3.…

A: Inverse Laplace transferom of the function

Q: 3. Find the polar coordinates of all points on the cardioidsr=1- sine, at which there is a…

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Q: The test scores of 20 students are listed below. Find the 34th percentile

A: We have to find the 34th percentile from the given data set.

Q: Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2+ 5n, express an in terms of n.

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Q: 1. Find the (a) true error and (b) relative error of the following: 1. The derivative of /(x) = x +…

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Q: Find an equation of the ellipse having a major axis of length 10 and foci at (-3, 3) and (- 3, – 3).

A: This is a problem of locus and analytical geometry.

Q: a. [(r ^ p) ^ (p ^ q)] →p b.For the given statement write as a conditional statement, then write…

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Q: The following table shows the length, in centimeters, of the humerus and the total wingspan, in…

A: We can solve this using linear regression formula

Q: 3 b.

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Q: Find the Laplace transform of: 1. f(t) = e(3t-7) cos (6t)

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Q: Find the work done by F over the curve in the direction of increasing t. F = -8x i + 9x 3y 4 j +…

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Q: 10s2+5s+4 F(s) (s³–6s²+11s-6)(s³)

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Q: Which of the followings is TRUE for f(x, y) = 3x – y + 6 on the circle a? + y? = 4. Lütfen birini…

A: Given function is fx,y=3x−y+6 and a circle is x2+y2=4. We have to find the maximum and minimum of…

Q: To help with the startup costs of his new dental practice, Tony is taking out a $56,000 amortized…

A: Loan Amount =$ 56,000 Interest rate =8.5% pa                     =8.5%12 Monthly payment =$694.32

Q: The volume produced by revolving about the x-axis the region above the curve y= x° below the line y…

A: To find  The volume produced by revolving about the X-axis the region above the curve and below the…

Q: Evaluate using Laplace Transform: f(t) = tcos 3t -dt e-4t

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Q: QUESTION 1 Which of the following is a general solution to the following 4x?y"+4xy'+ (4x2 – 25) y=0…

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Q: Find the centroid of the region. NOTE: Enter the exact answers. (a, 9) =| (?, ?) %3D y = x7 1

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Q: Describe the graph of the equation. r = 4 sin 6t i – 4 cos 6t j O It is a parabola in the xy-plane,…

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Q: i) Simplify sin(2sin-1x). ii) Show that sin 30 = 3 sin 0 – 4sin30. iii) By using the substitution 0…

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Q: Find the inverse transform of the given functions: 4s2 -4s+1 1. F(s) = (s3-4s2+s+6)(s²+5)

A: To solve given question first we write the partial fraction decomposition of given function and then…

Q: A = 6 B = 4 C= 6 D = 4 b) Solve for the value of ?1 c) Solve for the value of ?2

A: Here given A = 6, B = 4, C= 6, D = 4 Then graph becomes

Q: (6) The total differential of the function tan-1(x/y), where (x, y) (0,0) is ydx – xdy (a) x2 – y?…

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Q: 2e* xy" - (2x + 1)y' + (* + 1)y %3D * ond ex ore linearly indenerndent

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Q: Let f(z) = ((z – 3i)² + 9)ez- The Laurent series representation of f(z) in the domain 0 < |z – 3i| <…

A: Given function is fz=z−3i2+9e1z−3i. We have to find the Laurent's series representation of fz in the…

Q: 5s+3 6s 8 F(s) - (5s2+4s+1) s2+7 9.

A: The laplace transform formulas for e^(at)cos(bt) and e^(at)sin(bt) will be used in solving this…

Q: Justify whether the following sequence {an} and the series an converges. If yes, find its limit. (a)…

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Q: 15) After declining over the past century, the percentage of men aged 65 and older in the workforce…

A: As per the question we are given th following data table : And we have to find the best fit cubic…

Q: 6. If a series Eu, converges to the sum u then so does any series obtained from Lu, grouping the…

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Q: Find the Laplace transform of: 1. f(t) = e-3t) sin(2t) cos(3t) cosh(t)

A: Laplace transferom of the function

Q: 9) Obtain the neetilinear attarymptotes.of the cunve

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Q: F(s) = 5s+3 6s 8 9- - (5s2 +4s+1) s2+7 9

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Q: According to building specifications and physical measurements, the maximum weight that foundation…

A: If x is directly proportional to y, then it can be written that x ∝y or x=ky. Here, k is the…

Q: For each of the following series determine if the series converges or diverges. In(n) n n=2 n3 n=0…

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Q: 4. Fit the following data points using Newton's Divided Difference Interpolating polynomial. Round…

A: Given: The data points, x 0 2 4 6 8 10 12 f(x) 52.698 53.414 49.002 41.718 35.354 35.238 48.234…

Q: Let x(t) be the displacement of an object, attached to a vibrating vertical spring with one end…

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Q: Find the centroid of the region bounded by y? = 16x and y? = 32(x – 8). - NOTE: Enter the exact…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…