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]
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]
0 Divided by 0: Solve Limit Problems in Calculus, Part 1
If you’re like many Calculus students, you understand the idea of limits, but may be having trouble solving limit problems in your homework, especially when you initially find “0 divided by 0.” In this post, we’ll show you the techniques you must know in order to solve these types of problems. I. The idea of… [read more]
Limits – Substitution
This is the first thing you should always try: just plug the value of x into f(x). If you obtain a number (and in particular, if you don’t get $\dfrac{0}{0}$), you have your answer and are finished. In that case, these problems are completely straightforward. Example. Find $\displaystyle{\lim_{x \to 2}(x^3-5x + 7)}$. Solution. \begin{align*} \lim_{x… [read more]
3 Common Limit Problems You Must Know How to Solve
Are you having trouble solving Calculus limit problems, even though you understand the concept? In this post we explain three approaches you’ll use again and again, especially in problems where you initially get “0/0.” I. Factoring You’ll use this approach most often. For example, consider the problem $$\lim_{x \to 4}\dfrac{x^2 – 16}{x-4} = ?$$ If… [read more]
