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Find the Maclaurin series representation for f(x) = e¬*". Find the zeroth order Maclaurin series approximation for f(x). • On the same graph with the same interval and the same scale, choose a different color of ink. • Plot AT LEAST 10 ordered pairs. • Connect the ordered pairs with a smooth curve. • Comment on the approximation near x = 0. Find the first order Maclaurin series approximation for fe • On the same graph with the same interval and the same scale, choose a different color of ink. • Plot AT LEAST 10 ordered pairs. • Connect the ordered pairs with a smooth curve

Find the Maclaurin series representation for f(x) = e¬*". Find the zeroth order Maclaurin series approximation for f(x). • On the same graph with the same interval and the same scale, choose a different color of ink. • Plot AT LEAST 10 ordered pairs. • Connect the ordered pairs with a smooth curve. • Comment on the approximation near x = 0. Find the first order Maclaurin series approximation for fe • On the same graph with the same interval and the same scale, choose a different color of ink. • Plot AT LEAST 10 ordered pairs. • Connect the ordered pairs with a smooth curve

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 16E
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Find the zeroth, first and second order

Make a very careful graph of f(x) = e¬x • Use graph paper • Graph on the interval -0.5<xs0.5 and 0.75 sys1.25 • Scale the graph to take up the majority of the page • Plot AT LEAST 10 ordered pairs. • Connect the ordered pairs with a smooth curve. Find the Maclaurin series representation for f(x) = e¬X Find the zeroth order Maclaurin series approximation for f(x). • On the same graph with the same interval and the same scale, choose a different color of ink. • Plot AT LEAST 10 ordered pairs. • Connect the ordered pairs with a smooth curve. • Comment on the approximation near x = 0. Find the first order Maclaurin series approximation for f • On the same graph with the same interval and the same scale, choose a different color of ink. • Plot AT LEAST 10 ordered pairs. • Connect the ordered pairs with a smooth curve. • Comment on the approximation near x = 0. Find the second order Maclaurin series approximation for f«b-x • On the same graph with the same interval and the same scale, choose a different color of ink. • Plot AT LEAST 10 ordered pairs. • Connect the ordered pairs with a smooth curve. • Comment on the approximation near x = 0. Overall, compare the graphs of the functions with the successively higher order Maclaurin series. What can you conclude about the "fit" at x = 0? near x = 0? How does the fit change as you move further from x = 0? What could you project about the third order approximation?
Transcribed Image Text:Make a very careful graph of f(x) = e¬x • Use graph paper • Graph on the interval -0.5<xs0.5 and 0.75 sys1.25 • Scale the graph to take up the majority of the page • Plot AT LEAST 10 ordered pairs. • Connect the ordered pairs with a smooth curve. Find the Maclaurin series representation for f(x) = e¬X Find the zeroth order Maclaurin series approximation for f(x). • On the same graph with the same interval and the same scale, choose a different color of ink. • Plot AT LEAST 10 ordered pairs. • Connect the ordered pairs with a smooth curve. • Comment on the approximation near x = 0. Find the first order Maclaurin series approximation for f • On the same graph with the same interval and the same scale, choose a different color of ink. • Plot AT LEAST 10 ordered pairs. • Connect the ordered pairs with a smooth curve. • Comment on the approximation near x = 0. Find the second order Maclaurin series approximation for f«b-x • On the same graph with the same interval and the same scale, choose a different color of ink. • Plot AT LEAST 10 ordered pairs. • Connect the ordered pairs with a smooth curve. • Comment on the approximation near x = 0. Overall, compare the graphs of the functions with the successively higher order Maclaurin series. What can you conclude about the "fit" at x = 0? near x = 0? How does the fit change as you move further from x = 0? What could you project about the third order approximation?
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