Let i = fr* sin(x) dx. The approximation of I using the two-point Gaussian quadrature formula is: O -379.538 O 0.14661 O 0.45327 O 2.56125

Q: Let P(x) be the Lagrange interpolating polynomial of 1 f(x) = ; 2x² + 2 at the points xo = 0; x, = 1…

A: We will use La Grange interpolation

Q: A miniature quadcopter flies in a curve line from one point to another. Suppose that the path of the…

A: We have to find arc length L= ∫ab1+dydx2dx

Q: Let I = L,r* cos(x + 1) dx. The approximation of I using the two-point Gaussian quadrature formula…

A: The two point Gaussian quadrature formula is ∫abf(x)dx≈c1f(x1)+c2f(x2) . Here,…

Q: ) Find f'(0.75) for h=0.25 according to the Table, a) with the Forward difference formula b) with…

A: 1) Forward Difference method:               f'(x)=(f(xo+h) − f(xo))/ h              f'(0.75) = (…

Q: Let P(x) be the Lagrange interpolating polynomial of the function Ín(x=2) f(x) at the nodes x, = 3,…

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Q: S(x) = } 1s + 3(x – a) – (x – 2)² – 2(x – 2)³ S is a natural cubic spline O False O True

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Q: Suppose that the values of a smooth function fis known for x=0, 0.3, 0.6 and 1.2. Select the 3-…

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Q: The approximation of the root x' of the funetion f(x) = x* + x* – 2x² – 3x – 3 accurate to within…

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Q: Suppose "(1) = N;CN) + a,n^ + aga* + ayh* + -- When calculating N, (A) using Richardson…

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Q: The approximation of the root x* of the function f(x) = x*e* – 1 accurate to within 10-2 using…

A: To find  The approximation of the root of f(x) accurate to within 10^(-2) using Newton's method.

Q: Consider the initial value problem: t/yy'(t) = 2ty + 4y,/y, 1stS 1.2, y(1) = 1 %3D The approximation…

A: Given initial value problem is tyy'(t)=2t2y+4yy,    1≤t≤1, y(1)=1 step size h=0.1 We have to find…

Q: Romberg integration for approximating f(x) dx gives R21 = 4 and R22 = 12 then f (0)% = 14 O 5/2 17

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Q: Let P(x) be the Lagrange interpolating polynomial that fits the data (–2,3); (2,4) and (4, 3). Then…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find a, b and e so that the quadrature formula has the highest degree of precision [ f(x) dx =…

A: Solution :-

Q: Suppose f"(x) = N,(h) + a,h + azh³ + azh5 + .. The value of N2(h) using Richardson's extrapolation…

A: The value of N2(h) using Richardson's extrapolation is: N2 (h)=2N1 (h/2)-N1 (h) with error of order…

Q: Use Romberg integration to find an O(h*) approximation for the following integral 1= [ In(x² + 2)dx…

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Q: Q3 (a) A polluted pool has an initial concentration of bacteria of 10* part/m3, while the acceptable…

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Q: a-Solve the following system using Gaussian Elimination, using three digits arithmetic and rounding.…

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Q: The degree of precision of a quadrature formula whose error term is:f() is is:

A: Clearly from the given error term error is of order 3.

Q: The degree of precision of a quadrature formula whose error term is : f(® (3) is

A: I am solving this in step 2

Q: (Q4) A small business has weekly profits of P(x) = x² + 4x – 2e", where x is the number of units…

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Q: c) Solve the boundary value problem given as y" + = 1, with boundary conditions y'(0.5) = -0.0283,…

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Q: (2) Using the False position method with a, = 4, bo = 5 to estimate the solution of the equation x³…

A: See the attachment

Q: Use Romberg integration to compute R3,3 for the following integral cos x dx

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Q: Use Romberg integration to compute R3,3 for the following integral x cos x dx

A: Romberg integration is one of the way to approximate the value of definite integrals. In this…

Q: Romberg integration for approximating , f(x) dx gives R21 = 2 and R3 = 3 then f(0): O 5/2 O 14 О 17…

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Q: Romberg integration for approximating , f(x) dx gives R21 = 1 and R22 = 12 then f(0) = O 17 O 5/2 O…

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Q: Questions Consider the integral dx | The approximation of I using the two-point Gaussian quadrature…

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Q: Given the following set of linear equations: X1 +x2 +5x3 = -21.5 -3x1 + 6x2 +2x3 = -61.5 10x1 +2x2…

A: In gauss elimination all diagonal elements are one. Also the matrix is upper triangular. So for the…

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.