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

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.