Tag: Limits

It would be nice to be able to stay at my leisure, to have the balance and physical capacity to be a Jack-Of-All-Trades. I’m not saying I would have stayed and bummed from job to job, meeting people like Marina, seeing new situations, challenging culture. Having the option to do so would be ni...

Ultrarunning, an extreme form of long-distance running that typically involves races longer than the traditional marathon distance of 42.195 kilometers (26.2 miles), has gained immense popularity in recent years. Athletes in ultrarunning events cover distances ranging from 50 kilometers (31 miles) t...

(don’t forget to checkout the video too) Making too much money can cause problems… For example, if you make too much money you are no longer eligible to contribute to a Roth IRA. And most people know that Roth IRA’s are one of the best ways to put yourself ...

Should there be a cap on how old our public officials can be? According to a Pew Research Center survey, the answer for most Americans is yes. As of this writing, the President of the United States is 81 years old. He is running for reelection. Should President Biden be successful, he will b...

Cancer is a nasty word that all of us would never want to get one day. Neither would we want to wish it on anyone. It is a very depressing and sobering thought to either have cancer or know of a close friend/family member who has cancer. We rejoice with them, though, when the medical tests sho...

This additional side is equivalent to tangent of theta. Why? If we call this side say, Side C, tangent is defined as being the opposing side divided by the ajacent side, so tangent theta must be equal to Side C divided by the ajacent side, which in this case is just 1. ...

It’s a helpful way to visualize basic trigonometric functions. For the rest of this guide, we will be using radian notation, instead of the standard degree one you may be familiar with. As a reminder, any degree can be expressed in terms of a radian, with the core ratio being that 180 de...

In our previous article, we discussed the limit’s connection with the definition of continuity, and used it to clear up the answer to one last ambiguous case. It turns out that a limit is a lot like a regular function. When the limit plays nice, it behaves really like a regul...

In our previous article, we defined the limit using the concept of one-sided limits, and provided a more mathematically rigorous way to graphically determine if a limit exists or not. This is all well and good, but limits have a level of nuance that seems nonsensical at first, but makes more...

Let’s build on our understanding of limits, and explore why sometimes limits don’t exist. We’ll get to a satisfying explanation of why the limit as x approaches 4 in the above example doesn’t exist. But, like reading the rules of a board game before we first start playing,...