## 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]

## Computing Limits – Calculus Problem of the Week

This Calculus Problem of the Week focuses on computing limits. We guarantee that you will have exam questions very much like these, and so we encourage you to practice many of the various types so you’ll be fully ready. Detailed Solutions (a) Use Factoring to Find a Limit \(\displaystyle{\lim_{x \to 2}\dfrac{x^2 + 3x-10}{x-2} = ?}… [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]

## Limits at Infinity: What You Need to Know

Are you working with Limit at Infinity problems in Calculus? Let’s break ’em down and develop your understanding so you can solve them routinely for yourself. I. How to think about “going to infinity” • When you see $\displaystyle{\lim_{x \to \, \infty}}$, think: “The limit as x grows and grows, and Grows, and GROWS, …,… [read more]

## How to Solve Optimization Problems in Calculus

Need to solve Optimization problems in Calculus? Let’s break ’em down and develop a strategy that you can use to solve them routinely for yourself. Overview Optimization problems will always ask you to maximize or minimize some quantity, having described the situation using words (instead of immediately giving you a function to max/minimize). Typical phrases… [read more]

## 0 Divided by 0: Solve Limit Problems in Calculus, Part 2

In Part 1 of this series, we illustrated three of the most common tactics you must know to use in order to be able to solve limit problems in Calculus: (See Part 1 for details on those.) In this post, we’re going to look at two other tactics you’ll frequently need to invoke. I. Tactic… [read more]