Review 4/3

Today I decided to review parametric equations. To help me while I reviewed my notes I additionally watched a Khan Academy video helping explain what parametric equations actually are. 

https://www.khanacademy.org/math/precalculus/parametric_equations/parametric/v/parametric-equations-1

In the video it explains that both x and y are functions of time. Through the use of parametric equations we can determine the direction and path of an object. Additionally you can also determine a third parameter, Z, on a three-dimensional plane. You can also determine the slope of a tangent line, velocity functions, acceleration functions, and speed. 

I also google searched problems with their solutions to help me understand and practice. http://tutorial.math.lamar.edu/problems/calcii/parametriceqn.aspx 

Assignment #15

1) Anything raised to 0 is equal to one, therefore 0^0 = 1.

2)

          a- T5(x)= (x^2/2) + (x^3/6) + (x^4/24) + (x^5/120)

          b- T5(x) = (x^2) - (x^3/6) + (x^5/120)
       
          c- T5(x) = (-x^2/2) + (x^4/24)

Assignment #14

1- The man will never be able to catch up to the tortoise. As he continues to chase the tortoise to its initial position, it continues to move forward creating a new position. Because of this he will never be able to pass the tortoise. This is similar to Zeno's Paradox because in this paradox the man can never reach the wall. The man continues to half each of his steps. Since he continues to half each of his steps, he will never be able to reach the wall. If there is an infinite amount of time, the man will eventually catch up and over take the tortoise. Additionally the other man will eventually reach the wall.

2- I agree with the answer of .5. .5 is between 0 and 1. This gives an approximate idea of what the answer could be but it is impossible to know the exact answer. This is also related to what we have been learning because it relates to the alternating series. Thomsons lamp dilemma makes sense because there can be an infinite amount of answers.

Assignment #13

In order to find the volume of the solid when revolving f(x)=1/x around the x-axis you must do V=integral of (1/x)dx*π  [0,∞) V=(ln∞-ln(1))*π V=π

In order to find the surface area you do
Surface Area=((1-(x^-4)^1/2))dx from [1,∞)*π*ʃ1/(x^2)dx = ∞

This isn't a paradox because the volume of the solid approaches π as the functions continues unto ∞ and while the surface area does not approach a definite integer while the function continues to approach ∞.

Assignment #12

This what if is about the demographics of Fairies. It relates to the logistic curve with both human and fairy populations and how they increase or decrease in the environment. As the human population increases so does the fairy population. The fairies are also immortal, meaning they cannot die unless something learns how to kill them. As the human population increases the carrying capacity, eventually the population would decrease slightly and since there is a direct relation to the fairy population, but they are immortal, the fairy population levels off and stays at a specific population.

Assignment #11

1) Lectures are very large and move quite rapidly. I think that this is how lectures in college will occur. You will have to constantly be paying attention, making sure you take down each bit of information the professor states.

2) Some classes I would take during college would be Electrical Engineering and Computer Science, Mathematics, Finance, and other business classes. I think that when the professor posts their lecture online is extremely helpful because it allows you to go back in-case you missed any information, and can give you the ability to examine and go over your notes you took during the lecture thoroughly.

Assignment #10

1: Logistic equations are used to represent growth over time. These equations are used primarily to describe population growth within a specific area. Environments can only hold a specific amount of animals or people or other things because their materials are limited and do not continuously grow. Logistic equations solve this problem by creating a carrying capacity for these locations

2: The point is limited when it is divided in half. This point then becomes known as the point of maximum growth on the logistic curve.

3: First you separate the different variables allowing the equation to then be able to get integrated. If the variables are not separated then you cannot solve for those variables making the problem incomplete.