1. I buy two houses, both at the same price. I do not tell you what the price was. A year later I sell them. The sales price of one is 20 % higher than the purchase price. The sales price of the other one is 20 % lower than the purchase price. Did I gain money, lose money or neither? Le., is the total sales price bigger, smaller, or equal to the total purchase price? 2. I sell two houses, both at the same price. I do not tell you what the price was. I bought both houses a year ago. The sales price of one is 20 % higher than the purchase price. The sales price of the other one is 20 % lower than the purchase price. Did I gain money, lose money or neither? I.e., is the total sales price bigger, smaller, or equal to the total purchase price? 3. You need to explain your reasoning, based on your understanding of what "approaching'" means. You cannot use any derivative rules in this question: you need to recall how we got to the concept of the derivative using ARCS. Prof. May B. Wright calculates the ARCS 70+h)-f() of the function f(x) = x2, for h = +1, ±0.1, ±0.01, ±0.001, +0.0001. He gets the following table (as we have seen in class). h (fa+h) - f(@))/h a 1 -1 1 1 -0.1 1.9 1 -0.01 1.99 1 -0.001 1.999 1 -0.0001 1.9999 0.0001 2.0001 1 0.001 2.001 1 0.01 2.01 1 0.1 2.1 1 1 From this table he concludes: it looks like the ARCS are approaching 2.00000000001 as h approaches 0, both for positive and negative h. Therefore, f'(1) = 2.00000000001. Is he right or wrong? Why? %3D
1. I buy two houses, both at the same price. I do not tell you what the price was. A year later I sell them. The sales price of one is 20 % higher than the purchase price. The sales price of the other one is 20 % lower than the purchase price. Did I gain money, lose money or neither? Le., is the total sales price bigger, smaller, or equal to the total purchase price? 2. I sell two houses, both at the same price. I do not tell you what the price was. I bought both houses a year ago. The sales price of one is 20 % higher than the purchase price. The sales price of the other one is 20 % lower than the purchase price. Did I gain money, lose money or neither? I.e., is the total sales price bigger, smaller, or equal to the total purchase price? 3. You need to explain your reasoning, based on your understanding of what "approaching'" means. You cannot use any derivative rules in this question: you need to recall how we got to the concept of the derivative using ARCS. Prof. May B. Wright calculates the ARCS 70+h)-f() of the function f(x) = x2, for h = +1, ±0.1, ±0.01, ±0.001, +0.0001. He gets the following table (as we have seen in class). h (fa+h) - f(@))/h a 1 -1 1 1 -0.1 1.9 1 -0.01 1.99 1 -0.001 1.999 1 -0.0001 1.9999 0.0001 2.0001 1 0.001 2.001 1 0.01 2.01 1 0.1 2.1 1 1 From this table he concludes: it looks like the ARCS are approaching 2.00000000001 as h approaches 0, both for positive and negative h. Therefore, f'(1) = 2.00000000001. Is he right or wrong? Why? %3D
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:1. I buy two houses, both at the same price. I do not tell you what the price
was. A year later I sell them. The sales price of one is 20 % higher than
the purchase price. The sales price of the other one is 20 % lower than the
purchase price.
Did I gain money, lose money or neither? Le., is the total sales price bigger,
smaller, or equal to the total purchase price?
2. I sell two houses, both at the same price. I do not tell you what the price was.
I bought both houses a year ago. The sales price of one is 20 % higher than
the purchase price. The sales price of the other one is 20 % lower than the
purchase price.
Did I gain money, lose money or neither? I.e., is the total sales price bigger,
smaller, or equal to the total purchase price?
3. You need to explain your reasoning, based on your understanding of what
"approaching'" means. You cannot use any derivative rules in this question:
you need to recall how we got to the concept of the derivative using ARCS.
Prof. May B. Wright calculates the ARCS 0+h)-f() of the function f(x) =
x2, for h = +1, ±0.1, ±0.01, ±0.001, +0.0001.
He gets the following table (as we have seen in class).
h (fa+h) - f(@))/h
a
1
-1
1
1
-0.1
1.9
1
-0.01
1.99
1
-0.001
1.999
1
-0.0001
1.9999
1
0.0001
2.0001
1
0.001
2.001
1
0.01
2.01
1
0.1
2.1
1
1
From this table he concludes: it looks like the ARCS are approaching 2.00000000001
as h approaches 0, both for positive and negative h.
Therefore, f'(1) = 2.00000000001. Is he right or wrong? Why?
%3D
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