Prove that the following functions are Riemannian integral over the period [0,3 ] with finding the value of the integral f(x) = x² 2

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Q: [[F(x, R th limits of integration B D -IT² f(x, y) dA = f(r cos(0), r sin(0)) r dr de (Click on…

A: In this question, the limit of integration of polar coordinates is determined.…

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A: Introduction: In manage device engineering, the Laplace transformation is crucial. Laplace…

Q: T 2 r = 2 + 4 cos 0 Option 1 r = 2 + 4 sin 0 Option 3 axis? r=2-4 sin 0 Option 2 r=2 sin 30 Option 4

A: Which of the following is not symmetric with respect to the pi/2

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

Q: Evaluate 3 [¹²* * yª² sin zº dx dy dz 0

A: This is a problem of Triple Integration.

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A: Given: The elliptic curve, E:y2=x3+ax+b over some prime field Fp. The points; r,0, s,2 and t,3, are…

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A: The numerical solution of the differential equation is the value of the function that satisfies the…

Q: number 14

A: Given, z1=3 cis 40°z2=5 cis 20°  The product of complex number is to be determined.

Q: 3. Write matrices for an x-shear with shear factor -2, a rotation of 180, an enlargement of scale…

A: To Write: matrices for x-shear with shear factor -2, a rotation of 180°, an enlargement of scale…

Q: what is the rectangular form of the final answer?

A: Rectangular form of complex number x + jy

Q: Julian is making barbecue sauce that he will put into jars. He uses 15 cups of tomato sauce, 6 cups…

A: Given- Juiian is making barbeque sauce that he will put into jars. He uses 15 cups of tomato sauce,…

Q: Let Us Assess Take your time and study the figure below. Show your solution in calculating its area.…

A: Let us consider the rectangle of length L and breadth B  The area of rectangle is obtained as Area…

Q: M8 (2-3x)"

A: Given: Series ∑n=1∞2-3xnn3n To find: Sum of given series.

Q: Q6: Find the Fourier coefficients and Fourier series of the function f(x) defined by -H<x<0 f(x) =…

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Q: 4) USE THE GAUSS-JORDAN 2 0 -3 0 2 0 -4 1 A= 1 -1 1 - 3 0 2 1 - 4 || REDUCTION METHOD (SINE…

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Q: Suppose that an equilateral plate that is 2 feet high is standing straight on the bottom of a 6 feet…

A: We will find force on horizontal slice of plate and then integrate it to find total force . 56u

Q: Using any of the methods discussed for both numerical differentiation and numerical integration…

A: Given: ∫021xdx To find: Definite integral

Q: 11. Let R and R' be two rings. A mapping f: R→R' is called an antihomomorphism, if f(x+y)=f(x) +…

A: Let x, y ∈ R. Then (g)(x + y) = f(g(x + y)) = f(g(x) + g(y)) = f(g(x)) + f(g(y)) =(fg)(x)+(fg)(y),…

Q: The equation of a hyperbola given below when reduced to standard form is 16y² −9x² +36x + 96y - 36 =…

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Q: b) Let T:R³ R³ be a linear transformation, and let B = {e₁, e2, e3} be the standard basis for R³.…

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Q: c) Define the linear transformation T: R³ →R² by T([])= [² = ³6 ] a - 3c +b- Find a basis for the…

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Q: using appropriate calculus techniques, calculate furthest distance he could possibly travel on a…

A: This is a problem with the application of derivatives.

Q: Evaluate: 0 V|2 − r|+dr -2

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Q: Let (zn)n≥1 be a geometric progression of complex numbers, and suppose that z3 = −1 and z5 = 7. Find…

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Q: Description of task. 7. This is a method which involves using an iterative formula. You must…

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Q: Identify the line or segment as a radius, chord, diameter, secant, or tangent of L. 1. KM 2. LN M 3.…

A: We have: Part(1) KM=diameter

Q: Using the Euler-Lagrange equation of the Calculus of Variations Optimize (-16y2 + 144y + 11yy' -…

A: Solution: Given I=∫01-16y2+144y+11yy'-4y'2dx and y(0)=8 and y(1)=8.6 Now, By Euler Lagrange Equation…

Q: 9) x² + y² + 12x + 22y + 108 = 0 CX+67² + y +117²=49 CX-47² \ Cy-151²=9 CX-107² + (y +1272²=9 CX-5)…

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Q: Numerical Integration: S (2.². (2x² – 3x)dx 2. 2

A: Let, f(x) = 2x2 - 3x, We know that Simpson one third rule gives the accurate result up to third…

Q: By 28(1 + i√3) solve all of its z-values if it is raised to 14.

A: Solution : To find, 28(1+i3)14 =56eiπ3+2nπ0.25 where, n∈ℤ n=0,1,2,3 =2.74eiπ12+nπ2

Q: WRITTEN ONLY PLEASE FOR

A: Given,      ∫032-x+xdx

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A: As per our guidelines we are supposed to answer only one question and rest can be reposted Given:…

Q: et R={(x,y)=R² | x² + y² ≤4y}. Draw it. Write it in polar coordinates.

A: R=x, y∈ℝ2|x2+y2≤4y

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A: Given function as, It is between is -π and 5π2.   As per rule, allowed to answer first question and…

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Q: (D6 + 10D4+25D²)y = 0

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Q: Solve (D+1)y=z+ e* (D+1)z = y + e* y = Z=? [1] [2]

A: The system of Linear Equation are                           D+1y=z+ex......1D+1z=y+ex......2 To…

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A: Introduction: The distance between two places along a portion of a curve is called arc length.…

Q: Q#6 solve the BVP Give comments on the values of a? y" + y = 0 y(0) = 1, y(π) = = a

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Q: The eccentricity of the hyperbola given by the equation below is 16y² - 9x² + 36x + 96y - 36 = 0 √5…

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Q: Question 2: (a) Insert 4 arithmetic means between 1 and 15. (b) Insert 5 geometric means between 3…

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Q: A Fourier transform is another integral transform often used in higher mathematics. The Fourier…

A: As per the question we are given the definition of Fourier transform of f(t) as F(ω) Amd from that…