Taylor's formula with n=1 and a=0 gives the linearization of a function at x=0. With n = 2 and n=3 we obtain the standard quadratic and cubic approximations. Explore the errors associated with these approximations by answering two questions. (x)= a. For what values of x can the function be replaced by each approximation with an error less than 10"²? b. What is the maximum error to expect by replacing the function by each approximation over the specified interval? Using technology, perform the steps below to aid in answering these questions. Step 1: Plot the function over the specified interval. O A. OB. D. Step 2: Find the Taylor polynomials P₁(x). P2(x), and P3(x) at x=0. P₁(x)= P2(x)= P3(x)= Step 3: Calculate the (n+1)st derivative fin+1)(c) associated with the remainder term for each Taylor polynomial. Plot the derivative as a
Taylor's formula with n=1 and a=0 gives the linearization of a function at x=0. With n = 2 and n=3 we obtain the standard quadratic and cubic approximations. Explore the errors associated with these approximations by answering two questions. (x)= a. For what values of x can the function be replaced by each approximation with an error less than 10"²? b. What is the maximum error to expect by replacing the function by each approximation over the specified interval? Using technology, perform the steps below to aid in answering these questions. Step 1: Plot the function over the specified interval. O A. OB. D. Step 2: Find the Taylor polynomials P₁(x). P2(x), and P3(x) at x=0. P₁(x)= P2(x)= P3(x)= Step 3: Calculate the (n+1)st derivative fin+1)(c) associated with the remainder term for each Taylor polynomial. Plot the derivative as a
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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Transcribed Image Text:Taylor's formula with n=1 and a=0 gives the linearization of a function at x=0. With n = 2 and n=3 we obtain the standard quadratic and
cubic approximations. Explore the errors associated with these approximations by answering two questions.
(x)=
a. For what values of x can the function be replaced by each approximation with an error less than 10"²?
b. What is the maximum error to expect by replacing the function by each approximation over the specified interval?
Using technology, perform the steps below to aid in answering these questions.
Step 1: Plot the function over the specified interval.
O A.
OB.
D.
Step 2: Find the Taylor polynomials P₁(x). P2(x), and P3(x) at x=0.
P₁(x)=
P2(x)=
P3(x)=
Step 3: Calculate the (n+1)st derivative fin+1)(c) associated with the remainder term for each Taylor polynomial. Plot the derivative as a
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