yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Example of one sides unbounded limits


2m read
·Nov 11, 2024

We're asked to select the correct description. It looks like all the descriptions deal with what is the limit of f of x as we approach six from either the right-hand side or from the left-hand side.

So let's think about that. First, let me just do the left-hand side. The limit of f of x as we approach six from the left-hand side: what is this going to be equal to?

As we approach from the left-hand side, we can see, well, f of four is a little under two. f of five is looks like it's around three. f of 5.5 is looks like it's a lot higher. f of 5.75 even, it's just going off the chart. So it looks like this is going unbounded in the positive direction.

So we could say that this right over here is positive infinity. If we were to think about the limit of f of x as we approach 6 from the right side, what is this going to be?

Well, here f of seven, it's negative. f of 7.5 is even more negative. f of 6.5 is even more negative. Not 7. f of 6.5 is even more negative. f of 6.1 is way more negative than that. f of 6.01 would be even more negative than that.

So it looks like this is unbounded in the negative direction. So this is negative infinity.

Now let's see which of our choices match up to that. The way they listed it, they listed the limit from the right direction first. So that's this one: the limit of f of x as x approaches 6 from values greater than six, we have negative infinity.

So that is these two choices; these two choices say that. So we're going to rule out those two choices. Then we think about as we approach six from the left-hand side. We see that we go to positive infinity and that is this choice right over here.

So we rule out that one, and that is what we will pick.

More Articles

View All
Reject Most Advice
Regarding the guy that gets rich in five years, one of the tweets that you had on the cutting room floor was: avoid people who got rich quickly; they’re just giving you their winning lottery ticket numbers. This is generally true of advice anyway, which i…
What the Fahrenheit?!
As an Australian Canadian, the Fahrenheit temperature scale has always seemed a bit arbitrary to me. I mean, why does water freeze at 32 degrees? Why that integer? And what exactly does 0 represent? According to many sources, the Fahrenheit scale was defi…
Using recursive formulas of geometric sequences | Mathematics I | High School Math | Khan Academy
The geometric sequence ( a_i ) is defined by the formula where the first term ( a_1 ) is equal to -1⁄8 and then every term after that is defined as being so ( a_i ) is going to be two times the term before that. So, ( ai ) is ( 2 \times a{i-1} ). What is…
Learn to code in 60 seconds #programming #computerscience #python #khanacademy
Learn to code in 60 seconds. A program is a coded set of instructions for a computer to execute. Programs manipulate data, which come in several data types: integers, that’s whole numbers; floats, have decimal points; booleans, true or false; and strings,…
Cruise Ship Propulsion | Making the Disney Wish | Mini Episode 2
Our Disney Wish has a new propulsion system. This is definitely a used Azipod, which is an electric motor-driven propeller under the water. It really allows for some amazing performance. We’ve made the step from going from a conventional shaft line prope…
Can You Perceive Acceleration?
Have you ever considered how your eye scans across a landscape? I think most people assume that, like a video camera, it pans smoothly across the scene. But I don’t actually think that’s what happens. In truth, I think the eye jumps from image to image as…