1. Consider the curve C = {(x, y) € R²: x – y³ = 0}. Let ø: R → R be defined by (t) = t³, then o is a bijection from R to R and so it has an inverse o-1. The equation that defines C can be written as a = ¢(y), and by applying o-1 on both sides we obtain the equivalent equation y = 0-'(x). Therefore y is a function of r. Taking this into account, differentiating the equation y x = y° with respect to x on both sides yields 1 = 3y2 and y = 0 into the last equation yields 1 = 0. fip dr Since (0, 0) e C, plugging in r = 0 (a) Explain the mistake(s) in the above argument. (b) Explain why the Implicit Function Theorem cannot be used to fix the above argument.
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.
Solve questions 1a and b
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