Exercise 3.19 (TAYLOR polynomial) Provided is the function f : [-1, ∞) → R with f(x)=√1+x. a) Determine the TAYLOR polynomial T3(x) of order 3 with the expansion point xo = 0. b) Calculate an approximation value for √1.2 using T3(x). c) Give an estimation for the approximation error for 0 ≤ x ≤ 0.5 using the remainder.
Exercise 3.19 (TAYLOR polynomial) Provided is the function f : [-1, ∞) → R with f(x)=√1+x. a) Determine the TAYLOR polynomial T3(x) of order 3 with the expansion point xo = 0. b) Calculate an approximation value for √1.2 using T3(x). c) Give an estimation for the approximation error for 0 ≤ x ≤ 0.5 using the remainder.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.3: Change Of Basis
Problem 17EQ
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![Exercise 3.19 (TAYLOR polynomial) Provided is the function f : [-1,0) → R with
f(x) = V1+x .
a) Determine the TAYLOR polynomial T3(x) of order 3 with the expansion point xo = 0.
b) Calculate an approximation value for v1.2 using T3(x).
c) Give an estimation for the approximation error for 0 < x< 0.5 using the remainder.
Exercise 3.20 For a monopoly company producing a single good, we know the given data:
(i) Average variable costs (depending on output quantity x) are given by:
kv(x) = 0.5 x2 – 5 x + 25
-
(ii) Fixed costs (not averaged) are at K
= 6000.
(iii) For revenues E and price p there is a relationship:
E 3 400р — 0.4 p*, for p E [0, 100]
(a) At what quantity x and at what price p does the company attain maximum profit? What is the
level of that maximum profit?
209 - 10
(b) The owner of the company claims, that the quantity of minimum efficient scale (MES) is given by
x = 20. Is she right or wrong?
Hint: Total costs K are aggregated by fixed costs K and variable costs Ky, K = Kt + Ky. Average
variable costs kv are given by Kv/x.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F712a0eeb-dd38-40f6-97e7-0d7739c303f8%2Fe0b386cc-ec14-4cc8-a475-403dbdb2640a%2Fp5ek3pn_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 3.19 (TAYLOR polynomial) Provided is the function f : [-1,0) → R with
f(x) = V1+x .
a) Determine the TAYLOR polynomial T3(x) of order 3 with the expansion point xo = 0.
b) Calculate an approximation value for v1.2 using T3(x).
c) Give an estimation for the approximation error for 0 < x< 0.5 using the remainder.
Exercise 3.20 For a monopoly company producing a single good, we know the given data:
(i) Average variable costs (depending on output quantity x) are given by:
kv(x) = 0.5 x2 – 5 x + 25
-
(ii) Fixed costs (not averaged) are at K
= 6000.
(iii) For revenues E and price p there is a relationship:
E 3 400р — 0.4 p*, for p E [0, 100]
(a) At what quantity x and at what price p does the company attain maximum profit? What is the
level of that maximum profit?
209 - 10
(b) The owner of the company claims, that the quantity of minimum efficient scale (MES) is given by
x = 20. Is she right or wrong?
Hint: Total costs K are aggregated by fixed costs K and variable costs Ky, K = Kt + Ky. Average
variable costs kv are given by Kv/x.
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