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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, …, […]

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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 […]

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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) […]

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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 […]

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Related Rates Problem – Cylinder Drains Water

A student recently wrote to ask if we’d help solve a common related rates problem about water draining from a cylindrical tank. The problem was something like this: Cylinder Drains Water. A cylinder filled with water has a 3.0-foot radius and 10-foot height. It is drained such that the depth of the water is decreasing […]

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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 […]

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4 Steps to Solve Any Related Rates Problem – Part 2

In our last post, we developed four steps to solve any related rates problem. We introduced three examples to illustrate the basic ideas, and solved two of them there. As promised, we’ll solve the third here. Water Leaving a Cone Example Here’s the problem statement, now with some additional details about the cone itself and […]

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4 Steps to Solve Any Related Rates Problem – Part 1

Almost 90% of respondents find this blog post “very” or “extremely useful.” What about you? Please let us know below! Are you having trouble with Related Rates problems in Calculus? Let’s break ’em down and develop a strategy that you can use to solve them routinely for yourself. I. What’s related about these rates? (Or, […]

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Helping You with Calculus: Introducing Matheno

I created Matheno for one simple reason: to help students do well in their college-level science and math courses. As a former Physics faculty member at UC Berkeley, I’ve worked with many beginning students from diverse backgrounds. Most work hard to do well, and many succeed greatly. But others, despite the same amounts of time […]

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