Intro to limit properties

Added: 2026-05-16

[00:00:00]Welcome to the channel. So, today we're going to be, um, doing some, uh, limit problems, like continuing from, uh, some of past videos. And, uh, we're going to be looking at, um, some uh, limits uh, using, uh, this property up here, uh, with uh, sin x over x equals 1, cuz that's going to be needed, like, uh, trigonometry is going to be, uh, pretty heavily used in limits, as well. So, let's, uh, solve this problem. So, this is going to be pretty easy, right? So, uh, the so the x obviously cannot be zero, cuz we can't just make x zero here, cuz you're dividing by zero. So, [snorts] we're going to we can make 3x equal to y, right? Just to say y, and then this will be lim, uh, let's change this to y for now, y equals zero, and you'll see why. sin y over x will be equal to y over 3, right? So, we'll just replace that with y over 3. So, now, lim of uh, sin um So, uh, we're So, okay. Doing sin y divided by, um y over 3 is the same as multiplying by 3 over y, right? That's something that we know, right? So, um, that's going to just be 3 sin y over y, right? And y equals zero. See, it's the same thing, right? Just using different variables.

[00:01:17]So, this will cancel become 1, so it's 3 * 1 = 3. So, limit as y equals zero, x approaches zero here, equals 3. And that's it. Thank you.