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Love math and chemistry and often find myself procrastinating things I actually need to do by solving random problems I find on the internet. Interested in pursuing a PhD in bioinformatics or computational biology/chemistry at some point, but currently a candidate for becoming an Officer in the Army.

I began tutoring back in 2010 while I was still in high school for the teacher that I took General Chemistry with. In college, I was invited to be an Organic Chemistry study group leader for the University of North Texas (UNT). I worked with one of the local school districts in Lewisville, Texas with their Socratic based tutorial sessions. I also worked with the athletes at UNT as both a tutor and an academic coach. On the math side: I tutored classes for the athletes ranging from pre-Algebra up to Differential Equations and Linear Algebra. On the chemistry side: I tutored General and Organic Chemistry.

Starting my Masters' I began to TA and TF in the Math Department at UNT, while I continued my role as an Organic Chemistry study group leader. While in UNT's Math Department, I have taught or assisted with Algebra, pre-Calculus, Calculus I & II, Linear Algebra, and Differential Equations.

Each integral represents the volume of a solid. Describe the solid.

$ \pi \displaystyle \int_{0}^\pi \sin x dx $

In Example 3.8.1 we modeled the world population in the second half of the 20th century by the equation$ P(t) = 2560e^{0.017185t} $. Use this equation to estimate the average world population during this time period.

After an antibiotic taken is taken, the concentration of the antibiotic in the bloodstream is modeled by the function

$$ C(t) = 8(e^{-0.4t} - e^{-0.6t}) $$

where the time $t$ is measured in hours and $C$ is measured in $ \mu $g/mL. What is the maximum concentration of the antibiotic during the first $12$ hours?

The water level, measured in feet above mean sea level, of Lake Lanier in Georgia, USA, during 2012 can be modeled by the function$$ L(t) = 0.01441t^3 - 0.4177t^3 + 2.703t + 1060.1 $$where $t$ is measured in months since January 1, 2012. Estimate when the water level was highest during 2012.

Use the guidelines of this section to sketch the curve.

$ y = \frac{x}{x - 1} $

(a) Suppose that $ f $ is differentiable on $ \mathbb{R} $ has two roots. Show that $ f' $ has at lease one root.(b) Suppose $ f $ is twice differentiable on $ \mathbb{R} $ and has three roots. Show that $ f" $ has at least one real root.(c) Can you generalize parts $ (a) $ and $ (b) $?