MakeUp Blogs

Week 1 Prompt:
What concept do you feel like you mastered this nine weeks? What concept did you struggle with the most? Why? What can you change this nine weeks in your study habits, etc to improve your grade?

What have I mastered from the first nine weeks? Well, i feel that I have basically mastered most of the derivative rules. I understand how to do all of the complex chain, product, and quotient rules along with the definition of a derivative.

What did I struggle with? I really didn't have problems with much, one thing I still haven't learned is infinity limits, but that's because i don't feel like studying the different outcomes.

What can I change? I really need to start doing my homework and taking this class more seriously. Due to my failures to keep up with my studies I'm doing a ton of homework tonight including these make up blogs. So, I will start doing homework, blogs, and studying for tests to keep my grade in a good place.

Week 2 Prompt:
What are the steps to a related rate problem? What are the key words you look for and what do they mean? Give an example of a related rate problem and solve it.

Well, the steps are pretty simple. First off scan the problem and identify all given info. Next you should determine an equation to use for the problem. Next you implicitly differentiate your equation with respect to time. Finally you plug in your given info, and solve for whatever is needed to be solved for.

Key words to look for:
in respect to
rate of change
per

Ex. A 25ft ladder is leaning against a house. The base of the ladder is 7 feet away from the wall and is being pulled away from the wall at 2ft per second. How fast is the ladder moving down the wall?

First, Identify what is given. The height of the ladder, y, is not given but can be figured is 24ft. dy/dt is what we are looking for. The length of the ladder, c, is 25ft. dc/dt is 0 because it is not moving. The distance between the wall and the base, x, is 7ft. dx/dt is given and is 2ft/s.

The equation we will use is the Pythagorean theorem: x^2+y^2=c^2

Differentiate: 2x(dx/dt)+2y(dy/dt)=2c(dc/dt)

Plug in and solve for dy/dt:
dy/dt=7/6 feet per second.

Week 3 Prompt
What are the rules for simplifying exponents? What are the rules for simplifying logs?

This is probably one of my favorite things in math. Logs! There are many properties for logs and exponents. Exponent rules are pretty simple.

An exponent just means you multiply that number by itself the exponents number of times. More simply put: x^y is x times x, y times.
Some simple rules to remember when dealing with exponents:

The opposite of the exponent is the root.
x^-1=1/x^1
(x^2)(x^2)=x^4
(x^3)^2=x^6
(x^2)/(x^1)=x^1

Log rules:
The base of a log is 10 if not stated otherwise.
The base of a natural log is e.
loga+logb=log(ab)
loga-logb=log(a/b)
lne^a=a

There are more rules, but these are the rules that I feel are the most important as far as logs and exponents go.