1. Foundations

Calculus Review — Quiz

Test your understanding of calculus review with 5 practice questions.

Practice Questions

Question 1

If the rate of change of a drug's concentration in the bloodstream is given by the differential equation $\frac{dC}{dt} = -kC$, where $C$ is the concentration and $k$ is a positive constant, which of the following expressions represents the concentration $C(t)$ at time $t$ if the initial concentration is $C_0$?

Question 2

A biomedical engineer is analyzing the pressure distribution in a fluid, given by the function $P(x, y) = x^3y^2 - 2xy^3$. What is the partial derivative of $P$ with respect to $x$?

Question 3

In the context of modeling biological growth, if the growth rate of a population is proportional to its current size, which type of differential equation would best describe this phenomenon?

Question 4

A biomedical device's power output is described by $P(t) = 50 + 10\cos(\frac{\pi}{6}t)$ watts, where $t$ is time in hours. What is the instantaneous rate of change of power output at $t=3$ hours?

Question 5

Which of the following best describes the application of surface integrals in biomedical engineering?