Jann's DEV Project V0.Calculus

Heya everyone! Here's my 2nd DEV project! I hope everything is alright! =D

Q1: "The Valley of the Whatchamacallits"

In the planet called "Whatchamacallits", there is a 2D basic, parabolic valley where the villagers live. A genius named "MageYouLook" is a very wise wizard. He measured the valley covered by the village to be 1200 meters. In order to be the best in the whole planet, he needs to find the area of the land under the parabolic valley if the edge of the crust is 50 meters from the very bottom of the valley.

Solution:


Q2: "Water Drop"

One beautiful, sunny day, Ben got bored from playing an Online Game. He grabbed a cylindrical bucket and filled it with water. He put his finger right at the center of the bucket and he saw that it formed a circle that changes every second. Find the rate at which the radius changes per period of time, and the derivative formula of the equation of the circle when the radius is 45 centimeters.

Solution:


Q3: "Area Under the Curve" (You may NOT use a calculator for this problem)

Calculate the area enclosed by the derivative of the function ln (2x^2 + 3) on the interval
[0,4].

Solution:


Q4: "The Flibbermijibbit Bug"

Bugs from the land of Flibbermijibbits hate to touch the water. In the 2D land of the Flibbermijibbits, all the bugs follow a certain function as they move towards the water.

f(x) = x^2 + 3x + 2
x^2 + 2

Find the derivative formula of the function to determine how the movement of the bugs change with respect to time. Does the limit exist in this function?

Solution:


Reflection:

For me, making this project is a brilliant idea. It helps me and other ap students to learn more about calculus by creating our own questions and solving them. I had a little hard time making this project because there were other stuff to take care of. Creating the problem helped me review in my AP exam because it exercises what I have learned in class.