 # Intro to Limits and Continuity: A short Two Minutes Video

hey everyone my name is Sophie and I'm gonna today illustrate the concept of limits and continuity in a two-minute video I hope you enjoy it so let's consider the function of y equals 2x square let's see what happens to the value of y as the value of X approach 2 which means we want to see what happens if we get to the nearest point as possible to X equal to 2 let's try to do that from the right at first so as we can see here we get further and further to the nearest foreign from X equal to 2 and we see that the value of y approach for when X approach 2 from the right so if you wanna do the same thing from the left as we see we get further and further the value of y all supports 4 when X approach 2 from the left so in summary the limit of X square as X approach 2 from the right is equal to 4 where the positive sign beside the 2 means the right and the limit of X square and X approach 2 from the left is equal to 4 where the negative sign means the left so we can write these two equations together as the following because the limit from the left and the right are equal so we can say that the limit of X square as X approach 2 is equal to 4 note that this limit would be not exist if the limit from the left and the right are not the same so so we can note that the limit of X square as X approach 2 is equal to 4 and also the function of 2 is equal to 4 so because the function of 2 and the limit of X as X approach 2 is are equal the function is continuous so if the limit and the function are not equal then the function would not be continuous so thank you for watching and if you want more illustration or maybe a private session please visit the link under the video and click on request a lesson