S Use a Taylor polynomial with 4 nonzero terms to estimate 0 Estimate = Now estimate the error of the approximation. | error | ≤ 1 sin(0.8x) X -dx.

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx.

A: Given integral is ∫03 x3+xdx Number of sub-intervals = 6 Take f(x) = x3+x Step size  ∆x  = 3-06…

Q: Find the integral

A: Integrate∫3xx−2dx

Q: 8e X+7 3 tion has a root(s) at x~ bund until the final answer. Then round to six decimal places as…

A: We have to find the roots of  using preliminary analysis and graphing .

Q: Locate the first nontrivial root of sin(x) = x2 where x is in radians. Use bisection with the…

A: To do the calculations in Excel, first enter the numbers in separate cells. Each number is…

Q: b.) If r(x)= 1 √g(2x) > find r'(x) at x = 2

A: Topic = Derivative

Q: What is the local linearization of f(x) = arcsin(1+4x) near x = −1/4   arcsin(1+4x) ≈

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Q: Use Newton's method to approximate the maximum of f(x) = 2 sin x- with initial guesses of x = 2.5.…

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Q: X Let F(x) = ²* sin(6t²) dt. Find the MacLaurin polynomial of degree 7 for F(x). Use this polynomial…

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Q: Let P, (x) be the Legendre polynomial of degree n. Show that for any function, f(x), for which the…

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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: 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: a) Estimate the following definite integral numerically by using Simpson's rule. Take n=4 steps.…

A: Sol:- Simpson's Rule Approximation∫abfxdx ≈Δ x3fx0+4fx1+2fx2+4fx3+…+4fxn-2+fxn-1, where Δ x = b-an,…