Additional Question 6.4 A* : Evaluate the definite integral of x²e*^2 on he interval [0, 0.5] by using a McLaurin polynomial to represent the unction, and find the first n for which the error is guaranteed to be less han 0.001

Q: Which radical function has a domain of (xe Rx≤3) and range of (y e RIy2-4)? Oy--√x+3-4 Oy--√x+3+4…

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Q: Determine the stepsize that can be used in the tabu- lation of f (x) = sin x in the interval [0,…

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Q: the intepral Evaluate dr

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Q: Find all possible values of p∗ if p∗ approximates 0.25 × 10^−2 to at least 3 significant digits

A: To approximate : 0.25×10-2 up to 3 significant digits   0.25×10-2=0.0025

Q: Evaluate the integral Using residues and any e. other method which can be applied to solve this…

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Q: 77. Show that if f is a quadratic polynomial, then the SDQ at x = a (for any h + 0) is equal to…

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Q: Q.3 Find the value of x, for which the geometric n series Σ(3) (x + 4)" converges.

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple subpart…

Q: From the given data,identify f(4) using a Lagrance and Newton's polynomial…

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Q: Q2. Consider Xi 0.12 yi 0.7917 0.7733 0.7437 0.24 0.36 0.48 0.7041 0.6563 0.6023 0.60 0.72 Using…

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Q: 11. a. For the function f(x) = (3x+2), let x, =-1, x, =0, x, =1. Construct interpolating polynomial…

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Q: 3) Consider the definite integral [f(x) = √1+². calculate the following: a) Left hand sum using 2…

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Q: The error will disappear when using f(x)=x* to find the Lagrange interpolating polynomial p(x) if n…

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Q: Use Ay f'(x)Ax to find a decimal approximation of the radical expression. √√147

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Q: Find the equation for the family of quartic polynomials that have real roots of 3 (order 2) and 2 ±…

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Q: Use linear approximation to estimate √(4.01) + (4.01)2 correct to four decimal places.

A: Linear approximation of fx about x=a is given by L(x)=f(a)+(x-a)f'(a).

Q: π [25in 3 2Sin (3t+ π 7) dt

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Q: Suppose Q is a polynomial of degree n>= 2 with distinct roots, none lying on the real axis.…

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Q: .5 2. 2. dx =D dx- (6+z*) o o (x²+9)½ 's (x²+9)½

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Q: Differentiate the following function. y = In x+ In 5

A: The function is y = ln x + ln 5

Q: 3- Use the bisection method to find a root of the equation x² = -sin x in the interval [-1, 0] with…

A: Solution: The equation is x2=-sinx Rewrite it as x2+sinx=0 Let fx=x2+sinx Interval is -1,0

Q: Prove that Simpson’s Rule is exact when approximating the integral of a cubic polynomial function,…

A: Given function is ∫01x3dx Let f(x)=ax^3+bx^2+cx+d, where a,b,c,d are coeffients. Now calculate the…

Q: Evaluate the definite integrals correct to 4 significant figures by mid-ordinate method by six…

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Q: The function below has two roots between x = -6 and x = 10. Use the bisection method to estimate the…

A: We are given xex=1 so we have f(x)=xex-1 here we have x -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10…

Q: ∫((1/t)+6th root of t)dt

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Q: 9. Estimate the error in approximating sin(0.5) by using the fifth-degree Maclaurin polynomial by…

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Q: Find Newton’s polynomial that interpolates f(x) = x1 at x = 1, x=2,x=4,andx=5.…

A: Since, function is not clear so we assume fx=1x. We have to find the Newton's polynomial that…