I am a mathematical physicist currently pursuing a Doctoral degree at Queen's University. I have previously completed a Master's degree at l'Université de Montréal in Astronomy and Astrophysics. I have a passion for teaching and science outreach. During my undergraduate and postgraduate studies, I have enjoyed fulfilling teaching assistant positions. In addition, I have been a volunteer and coordinator for Let's Talk Science (Queen's University branch), promoting STEM outreach to youths in the Kingston, Ontario region. I am looking forward to further expanding my teaching experiences.
If $f(x)=x+\sqrt{2-x}$ and $g(u)=u+\sqrt{2-u},$ is it true that $f=g ?$
If $ f(x) = 3x^2 - x + 2 $ , find $ f(2) $ , $ f(-2) $ , $ f(a) $ , $ f(-a) $ , $ f(a + 1) $ , 2 $ f(a) $ , $ f(2a) $ , $ f(a^2) $ , $ [ f(a) ]^2 $ , and $ f(a + h) $.
Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).
$ \displaystyle \lim_{x \to 3}\frac{x^2 - 3x}{x^2 - 9} $,$ x $ = 3.1, 3.05, 3.01, 3.001, 3.0001, 2.9, 2.95, 2.99, 2.999, 2.9999
In the theory of relativity, the mass of a particle with velocity $ v $ is$$ m = \frac{m_0}{\sqrt{1 - v^2/c^2}} $$where $ m_0 $ is the mass of the particle at rest and $ c $ is the speed of light. What happens as $ v \to c^- $?
If the recommended adult dosage for a drug is $ D $ (in mg), then to determine the appropriate dosage $ c $ for a child of age $ a $ , pharmacists use the equation $ c = 0.0417D ( a + 1) $. Suppose the dosage for an adult is 200 mg.
(a) Find the slope of the graph of $ c $. What does it represent?(b) What is the dosage for a newborn?
In the theory of relativity, the Lorentz contraction formula $$ L = L_0 \sqrt{1 - v^2/c^2} $$expresses the length $ L $ of an object as a function of its velocity $ v $ with respect to an observer, where $ L_0 $ is the length of the object at rest and $ c $ is the speed of light. Find $ \displaystyle \lim_{v \to c}-L $ and interpret the result. Why is a left-hand limit necessary?
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval.
$ \ln x = x - \sqrt{x} $, $ (2, 3) $
Find the length of the curve correct to four decimal places. (Use a calculator to approximate the integral.)
$ r(t) = \langle \cos \pi t, 2t, \sin 2 \pi t \rangle $ , from $ (1, 0, 0) $ to $ (1, 4, 0) $
Find the smallest integer (a) such that the Intermediate Value Theorem guarantees that f(x) has a zero on the interval [0, a].f(x) = -8x^2 + 8x + 6
A rectangular box is to have a square base and a volume of 36 ft³. If the material for the base costs $0.18/ft², the material for the sides costs $0.12/ft², and the material for the top costs $0.14/ft², determine the dimensions (in ft) of the box that can be constructed at minimum cost.
A firm has monthly average costs, in dollars, given byC = 41,000/x + 300 + xwhere x is the number of units produced per month. The firm can sell its product in a competitive market for $2100 per unit. If production is limited to 550 units per month, find the number of units that gives maximum profit.x = unitsFind the maximum profit.$
Texts: Price of PerfumeThe monthly demand for a certain brand of perfume is given by the demand equation:p = 100e^(-0.0002x) + 100where p denotes the retail unit price (in dollars/bottle) and x denotes the quantity (in 1-oz bottles) demanded.
(a)Find the rate of change of the price per bottle (in dollars) when x = 2,000 and when x = 3,000. (Round your answers to four decimal places.)x = 2,000 dollars/bottlex = 3,000 dollars/bottle
(b)What is the price per bottle (in dollars) when x = 2,000? When x = 3,000? (Round your answers to the nearest cent.)x = $2,000x = $3,000
