It’s called Chebyshev’s Method for Bounding ϑ(x)/x. Now, if you don’t know what the ***** I’m talking about, let me explain in simple terms: this method helps us figure out how close a function gets to its limit as x approaches infinity (or minus infinity).

But why would we care about that? Well, for starters, it can help us solve some pretty tricky problems. For example, imagine you’re trying to find the value of pi using an infinite series. You might use Chebyshev’s Method to estimate how close your answer is to the actual value of pi (which we know is approximately 3.14).

Now, before I get into the details, let me give you a quick rundown of what this method involves: first, we find two functions that bracket our target function (in other words, one function will be greater than or equal to it and another function will be less than or equal to it). Then, we use these functions to create an interval around the true value. Finally, we calculate a bound for this interval using Chebyshev’s inequality.

Sounds complicated? Well, let me break it down even further: imagine you have two numbers, say 1 and 2. Now, if you want to find out whether these numbers are close together or far apart, you can use the following formula: |x-y| <= (b-a)/4 This is called Chebyshev's inequality, and it tells us that the distance between any two points in an interval of length b-a cannot be greater than one fourth of the width of that interval. So if we have a function f(x) that approaches some limit L as x goes to infinity (or minus infinity), we can use Chebyshev's Method to find bounds for this limit by finding two functions g(x) and h(x) such that: g(x) <= f(x) <= h(x) for all x greater than or equal to some value a (or less than or equal to some value b). Then, we can use Chebyshev's inequality to find bounds for the difference between these functions and our target function: |f(x)-L| <= |g(x)-h(x)| + |h(x)-L| This gives us an upper bound on how far away f(x) can be from L, which is useful if we want to know whether our approximation is good enough. And that's it! Chebyshev's Method for Bounding ϑ(x)/x may not sound like much at first glance, but trust me: once you get the hang of it, you'll be amazed at how powerful and versatile this tool can be. So give it a try! Who knows? You might just discover something new about math that will blow your mind (or at least make you chuckle).