What function f(x, y) gives e^((−.01)(.02)) when evaluated at (−.01, .02). At what nearby point (x0, y0) can one reasonably compute the value of f(x0, y0) without using a calculator. (b) Find the tangent plane p1(x, y) of f(x, y) from part (a) at the point (x0, y0). (c) Find the second order Taylor approximation p2(x, y) of f(x, y) from part (a) at the point (x0, y0).

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.EA: Extended Application Managing Renewable Resources
Problem 2EA
icon
Related questions
Question

(3) The goal of this problem is to approximate e^((−.01)(0.02)) .

(a) What function f(x, y) gives e^((−.01)(.02)) when evaluated at (−.01, .02). At what nearby point (x0, y0) can one reasonably compute the value of f(x0, y0) without using a calculator.

(b) Find the tangent plane p1(x, y) of f(x, y) from part (a) at the point (x0, y0).

(c) Find the second order Taylor approximation p2(x, y) of f(x, y) from part (a) at the point (x0, y0).

(d) Evaluate p1(−.01, .02) and p2(−.01, .02) by hand. Using a calculator, the first four decimal places of e^((−.01)(.02)) is 0.9998. Which gave a better approximation p1 or p2?

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Rate of Change
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Functions and Change: A Modeling Approach to Coll…
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning