Estimating   using a Taylor polynomial about  , what is the least degree of the polynomial that assures an error smaller than  ?Choose 1 answer:Choose 1 answer:(Choice A)    A (Choice B)    B (Choice C)    C (Choice D)    D

Does Taylor's Theorem with Remainder guarantee that the second Taylor polynomial at x=3 has an error less than 0.0001 in the estimate of 10e3.4 ?

Does Taylor's Theorem with Remainder guarantee that the second Taylor polynomial of f(x)=8ex at x=2 has an error less than 0.1 in the estimate of 8e2.3 ?

Suppose that you are estimating √7 using the second Taylor polynomial for √x at x=6 . Use Taylor's Theorem for Remainders to bound the error.Round your answer to six decimal places.Provide your answer below:

4 Third order derivative.a. Use Taylor series to derive the truncation error of the approximationf′′′(x) ≈( −f(x − 2h) + 2f(x − h) − 2f(x + h) + f(x + 2h))/2h^3assuming f ∈ C^5.b. Explain why dividing by h produces no roundoff error if h = 2−k, k ∈ N.c. Assuming that built-in functions return exact answers but that addition/subtraction produce roundoff errors and that h = 2^−k, k ∈ Z, show that the roundoff error RE in computing this expression satisfies the bound |RE| ≤ (K1 + K2h)u/h^3 where K1, K2 depend on f and x. You may use using the bound |θn| <nu/ (1 − nu)d. Hence estimate, in terms of u, the optimal choice for h.

Compute the relative error in approximating with 4 and express the result as apercentage.© 4.024994e-4 © 4.024994 x 10-2 O 4.024994e7? © 4.024994 x 107!