When you’re solving for a limit and you have a jump on the graph the limit will never exist. The limit will never exist because the graph will never be the same. If on one side of a graph may be going to positive infinite but the other may be going to negative infinite. Therefore the graph will never match which is why the limit will never exist at a jump. For an asymptote will sometimes have a limit depending on the graph. If one side of the graph is going down to negative infinite the other side must go down to negative infinite also for it to have a limit but, if one side of the graph is going up to positive infinite and the other side is going down to negative infinite then the graph will not have a limit making it does not exist. This is why an asymptote might have a limit. A removable will always have a limit. It will always have a limit because the graph will always be approaching the same thing from both sides.
While doing limits, there are some types of graphs that have limits and some that dont. A jump will never have a limit because it has two different y-values. With a jump this happens because the point jump from one graph to the next. Sometimes a limit exists in asymptotes. The limit will exist if it approaches the same way, but if it one side is approaching a negative and the other side is approaching a positive then there is no limit. A removable always has a limit. In a removable, you can plug a hole into the graph or remove because both sides are approaching the same thing.
Limits: A jump will never have a limit. The reason for this is because a jump will always have two different y-values. An asymptote may or may not have a limit because in an asymptote both sides can either both approach ∞ or both sides approach -∞. If the two sides approach different things then the limit does not exist. A removable will always have a limit, simply because in a removable, no matter what both sides of the graph will ALWAYS approach the same number.
a) A jump will never have a limit. This is because the graph does just that... it jumps from one coordinate to another. When a jump occurs, there is a gap in the graph, making a limit impossible. If you trace the graph coming from the right and get a limit, it will NEVER match up with the limit as you approach from the left, which means the limit does not exists. If these two limits never match up, then the answer will always be does not exist, so a jump will NEVER have a limit. b) An asymptote can have a limit sometimes. It all depends on what the graph approaches from the right and from the left. It will always approach either infinity or negative infinity from the left and right. What makes it have a limit though is whether it approaches the same thing from the left and right. If both the left and right approach positive infinity, or if they both approach negative infinity, then it has a limit….infinity or negative infinity depending on what they approach. But if from one side it approaches negative infinity, and from the other side it approaches positive infinity, then the limit does not exist. c) A removable always has a limit because all it is is a point removed from the graph. A removable does not change the graph in any way. When finding the limit of a line the little open circle called a removable can almost be ignored, because it will ALWAYS have a limit.
A. When there is a jump in the graph the limit will never exist. This because the right side of the graph and the left side of the graph does not match. there is a jump in the graph because the two points are different. there is no way you could have a limit with a problem like this.
B. an asymptote sometimes has a limit. this all depends on whether the asymptotes approach the same number or not. if the aymptotes are going the same way and they match each other the limit will exist. if they are going different ways and approaching different numbers the limit does not exist.
c. a removable will always have a limit. this is because if there is a removable they will always approach the same number. both sides always lead to the same thing.
a) A jump NEVER has a limit because it has two different points on the graph and you could never possibly have a limit. Also, because it is on the same x value.
b) An assymptote SOMETIMES has a limit. The assymptote has to approach the same number to have a limit. If they are both going the same way then the limit exists, but if not, then it does not have a limit.
c) A removable ALWAYS has a limit. If there is a removable, the graph will always approach the same thing from both sides.
A jump never has a limit- When there is a jump in the graph the limit will never exist. This because the right side of the graph and the left side of the graph does not match so it is DNE. There is a jump in the graph because the two points are different.
An asymptote sometimes have a limit-an asymptote will sometimes have a limit depending on the graph. If one side of the graph is going down to negative infinite the other side must go down to negative infinite also for it to have a limit but, if one side of the graph is going up to positive infinite and the other side is going down to negative infinite then the graph will not have a limit making it does not exist.
A removable always has a limit- a removable always has a limit because all it is is a point removed from the graph.
When you’re solving for a limit and you have a jump on the graph the limit will never exist. The limit will never exist because the graph will never be the same. If on one side of a graph may be going to positive infinite but the other may be going to negative infinite. Therefore the graph will never match which is why the limit will never exist at a jump. For an asymptote will sometimes have a limit depending on the graph. If one side of the graph is going down to negative infinite the other side must go down to negative infinite also for it to have a limit but, if one side of the graph is going up to positive infinite and the other side is going down to negative infinite then the graph will not have a limit making it does not exist. This is why an asymptote might have a limit. A removable will always have a limit. It will always have a limit because the graph will always be approaching the same thing from both sides.
ReplyDeleteWhile doing limits, there are some types of graphs that have limits and some that dont. A jump will never have a limit because it has two different y-values. With a jump this happens because the point jump from one graph to the next. Sometimes a limit exists in asymptotes. The limit will exist if it approaches the same way, but if it one side is approaching a negative and the other side is approaching a positive then there is no limit. A removable always has a limit. In a removable, you can plug a hole into the graph or remove because both sides are approaching the same thing.
ReplyDeleteLimits:
ReplyDeleteA jump will never have a limit. The reason for this is because a jump will always have two different y-values. An asymptote may or may not have a limit because in an asymptote both sides can either both approach ∞ or both sides approach -∞. If the two sides approach different things then the limit does not exist. A removable will always have a limit, simply because in a removable, no matter what both sides of the graph will ALWAYS approach the same number.
a) A jump will never have a limit. This is because the graph does just that... it jumps from one coordinate to another. When a jump occurs, there is a gap in the graph, making a limit impossible. If you trace the graph coming from the right and get a limit, it will NEVER match up with the limit as you approach from the left, which means the limit does not exists. If these two limits never match up, then the answer will always be does not exist, so a jump will NEVER have a limit.
ReplyDeleteb) An asymptote can have a limit sometimes. It all depends on what the graph approaches from the right and from the left. It will always approach either infinity or negative infinity from the left and right. What makes it have a limit though is whether it approaches the same thing from the left and right. If both the left and right approach positive infinity, or if they both approach negative infinity, then it has a limit….infinity or negative infinity depending on what they approach. But if from one side it approaches negative infinity, and from the other side it approaches positive infinity, then the limit does not exist.
c) A removable always has a limit because all it is is a point removed from the graph. A removable does not change the graph in any way. When finding the limit of a line the little open circle called a removable can almost be ignored, because it will ALWAYS have a limit.
A.
ReplyDeleteWhen there is a jump in the graph the limit will never exist. This because the right side of the graph and the left side of the graph does not match. there is a jump in the graph because the two points are different. there is no way you could have a limit with a problem like this.
B. an asymptote sometimes has a limit. this all depends on whether the asymptotes approach the same number or not. if the aymptotes are going the same way and they match each other the limit will exist. if they are going different ways and approaching different numbers the limit does not exist.
c.
a removable will always have a limit. this is because if there is a removable they will always approach the same number. both sides always lead to the same thing.
a) A jump NEVER has a limit because it has two different points on the graph and you could never possibly have a limit. Also, because it is on the same x value.
ReplyDeleteb) An assymptote SOMETIMES has a limit. The assymptote has to approach the same number to have a limit. If they are both going the same way then the limit exists, but if not, then it does not have a limit.
c) A removable ALWAYS has a limit. If there is a removable, the graph will always approach the same thing from both sides.
A jump never has a limit- When there is a jump in the graph the limit will never exist. This because the right side of the graph and the left side of the graph does not match so it is DNE. There is a jump in the graph because the two points are different.
ReplyDeleteAn asymptote sometimes have a limit-an asymptote will sometimes have a limit depending on the graph. If one side of the graph is going down to negative infinite the other side must go down to negative infinite also for it to have a limit but, if one side of the graph is going up to positive infinite and the other side is going down to negative infinite then the graph will not have a limit making it does not exist.
A removable always has a limit- a removable always has a limit because all it is is a point removed from the graph.