Look at the pictures please! 6) Let P4(x) = 7 – 3(x – 4) + 5(x – 4)² – 2(x – 4)3 + 6(x – 4)+ be the Taylor polynomial ofdegree 4 for the function f(x) centered around x = 4. It is known that |f(5) (x)| < 24 for all x inthe interval [4, 4. 3]a) Find the values of f(4) and f'''(4).b) Approximate f(4.3) using the 4th degree Taylor polynomial given above. What is themaximum possible error in making this estimate? Give FOUR decimal place accuracy for boththe approximate value and the error bound.c) Use your answer to part b) to find an interval [a, b] such that a < f(4.3) < b. GiveFOUR decimal place accuracy in all number values. 7) Let f be the function defined by f(x) =1+xa) Write the first four terms and the general term of the Maclaurin series for f(x)centered at x = 0.b) Find the interval of convergence for the Maclaurin series for f(x).c) Use the result from part a) to find the first four terms and the general term of theseries for g(x) = In |1 + x| centered at x = 0.[HINT: How can you get to In |1+x| from ?]1+xd) Find the interval of convergence for the series you created in part c).

Name: Look at the pictures please! 6) Let P4(x) = 7 – 3(x – 4) + 5(x – 4)² –
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Look at the pictures please! 6) Let P4(x) = 7 – 3(x – 4) + 5(x – 4)² – 2(x – 4)3 + 6(x – 4)+ be the Taylor polynomial ofdegree 4 for the function f(x) centered around x = 4. It is known that |f(5) (x)| < 24 for all x inthe interval [4, 4. 3]a) Find t