i was just wondering if the limit of a funtion exists as it approches a value if both the right side limit and the left side limit both equal the same infinity ( postive inififnty for both sides, or negative infinty for both sides).
i know that if one side is negative infinity and the other side is postive infinity the limit does not exist. But since in this situation both infinties are parrallel, i don't know the answer.
Thank you for your help!
Does infinity exist? No. Therefore the limit does not exist.
I am wondering what you mean by both infinities are parallel, I assume you did not mean that.
by that i meant that the inifnity for both sides of the x value,are both postive or oth nergative.
so the answer is no because for exaple even if the left side limit and the right side limit are both postive infinty, since we don't know the value for infinity the limit does not exist.
is that right?
To determine if the limit of a function exists as it approaches a value, we need to consider the behavior of the function as it approaches that value from both the left and right sides.
When both the left-side limit and the right-side limit of a function equal the same positive infinity or negative infinity, it indicates that the function grows without bound in both directions as it approaches that value. In this case, we say that the limit of the function is either positive or negative infinity, depending on the sign.
Therefore, if both the left and right-side limits approach positive infinity or negative infinity in a parallel manner, the limit does exist, and it is either positive infinity or negative infinity.
On the other hand, if one side approaches positive infinity while the other side approaches negative infinity, or vice versa, the left-side limit and the right-side limit are not equal, and the limit does not exist.
In summary:
- If both the left and right-side limits approach the same positive infinity or negative infinity, the limit exists and is positive infinity or negative infinity, respectively.
- If one side approaches positive infinity while the other side approaches negative infinity, or vice versa, the limit does not exist.
Remember to consider the behavior of the function from both sides to determine the existence and value of the limit.