Anthony Han is a senior at Bethlehem Central High School deeply interested in biochemistry, organic chemistry and biophysics who also enjoys the applications of calculus and differential equations. He is an enthusiastic subscriber to his school’s Science Bowl and Science Olympiad clubs and is a 3x - USABO semifinalist and a 2x - USNCO semifinalist (+ Top 150 Honors). He’s planning on attending Johns Hopkins University in the fall, majoring in biomedical engineering (and possibly chemical engineering). He hopes to pursue a career in research or the medical field, specializing in the development of immunotherapies.
Evaluate the limit, if it exists.
$ \displaystyle \lim_{x \to 5}\frac{x^2 - 6x + 5}{x - 5} $
$ \displaystyle \lim_{t \to -3}\frac{t^2 - 9}{2t^2 + 7t + 3} $
$ \displaystyle \lim_{x \to 3}\frac{\frac{1}{x}-\frac{1}{3}}{x - 3} $
$ \displaystyle \lim_{h \to 0}\frac{(x + h)^3 - x^3}{h} $
Evaluate the limit and justify each step by indicating the appropriate properties of limits.
$ \displaystyle \lim_{x \to \infty} \dfrac{2x^2 - 7}{5x^2 + x -3} $
Find the limit or show that it does not exist.
$ \displaystyle \lim_{x \to \infty}\frac{1 - x^2}{x^3 - x + 1} $
What are the main differences between theories and laws?
The demand function for a company is given by q=f(p)=3000-125p , with p the price in thousands of rands and q the quantity of items. Use the first derivative test and a number line to find the quantity that maximises revenue.
Which of the following is not a vector quantity?Group of answer choices
speed
Force
Impulse
Momentum
The unit kg.m/s is for:
Speed
Acceleration
A car (mass = 1,083 kg) is traveling at 25.2 m/s when it collides headon with a sport utility vehicle (mass = 2,930 kg) traveling in the opposite direction. In the collision, the two vehicles come to a halt. At what speed was the sport utility vehicle traveling?
Object A is moving due east, while object B is moving due north. They collide and stick together in a completely inelastic collision. Momentum is conserved. Object A has a mass of mA = 16.2 kg and an initial velocity of v0A = 8.56 m/s, due east. Object B, however, has a mass of mB = 26.5 kg and an initial velocity of v0B = 4.66 m/s, due north. Find the magnitude of the total momentum of the two-object system after the collision.
