## Function with Given Properties – Problem of the Week

Function with Given Properties – Calculus Problem of the Week This Calculus Problem of the Week exemplifies a type of college-level exam problem that appears from time to time, and involves the definition of the derivative. It is unlike most homework problems that you will have done. (You know how some teachers love to throw… [read more]

## Differentiability & Continuity – Problem of the Week

Differentiability and Continuity – Calculus Problem of the Week This Calculus Problem of the Week is a typical exam question that tests your understanding of differentiability versus continuity, and your ability to recognize the Definition of the Derivative and what it tells you. It’s also typical of a “which of these statements is/are true?” question…. [read more]

## Discontinuities & Asymptotes – Problem of the Week

Discontinuities and Asymptotes – Calculus Problem of the Week This Problem of the Week is requires finding the discontinuities and vertical and horizontal asymptotes of a rational function. It’s based on several typical exam questions of this sort. Let’s get right to it! Solution. Note: There’s a graph of the function at the bottom of… [read more]

## Definition of the Derivative – Problem of the Week

Typical Calculus Exam Problem: Definition of the Derivative This week’s problem is a typical exam question that requires using the Definition of the Derivative to first find the value of a function’s derivative at a given point, and then use that value to write the equation for the tangent line to the curve at that… [read more]

## Removable Discontinuity – Problem of the Week

Typical Calculus Exam Question: Continuity This Problem of the Week is a typical exam question about continuity, in particular about a removable discontinuity. You should expect a similar one on your exam(s), since it combines what we’ve been practicing to compute limits with the idea of continuity. Detailed Solution The key realization for this type… [read more]

## Limits from a Graph – Calculus Problem of the Week

This Calculus Problem of the Week (PoW) focuses on determining limits from a graph. These questions are meant as a quick check of your understanding, and mimic the type of typical question you’ll find on a college-level or AP®-style exam. As multiple-choice questions you get immediate quick feedback, and then more detailed solutions and discussion… [read more]