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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]

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Evaluating Limits

Evaluating Limits: Problems and Solutions You probably already understand the basics of what limits are, and how to find one by looking at the graph of a function. So we’re going to jump right into where most students initially have some trouble: how to actually evaluate or compute a limit in homework and exam problems,… [read more]

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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: In this post, we’re going to look at two other tactics you’ll frequently need to invoke. I. Tactic #4: Algebraic manipulation (dust off those skills)… [read more]

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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]

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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]

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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]

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Update September 2022

All of our content is now free, with the goal of supporting anyone who is working to learn Calculus well.

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