# Do limits exist at Asymptotes?

**asymptote**is a place where the function is undefined and the

**limit**of the function

**does**not

**exist**. This is because as 1 approaches the

**asymptote**, even small shifts in the x -value lead to arbitrarily large fluctuations in the value of the function.

Moreover, is an asymptote a limit?

A one-sided **limit** is a **limit** in which x is approaching a number only from the right or only from the left. An **asymptote** is a line that a graph approaches but does not touch. An **asymptote** that is a vertical line is called a vertical **asymptote**, and an **asymptote** that is a horizontal line is called a horizontal **asymptote**.

**exists**if and only if it is equal to a number. Note that ∞ is not a number. For example limx→01x2=∞ so it doesn't

**exist**. When a function approaches

**infinity**, the

**limit**technically doesn't

**exist**by the proper definition, that demands it work out to be a number.

Also to know, how do you know if a function has a Asymptote?

**The horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator.**

- Degree of numerator is less than degree of denominator: horizontal asymptote at y = 0.
- Degree of numerator is greater than degree of denominator by one: no horizontal asymptote; slant asymptote.

**Asymptotes**. An **asymptote** is a line that a **graph** approaches without touching. If a **graph** has a horizontal **asymptote** of y = k, then part of the **graph** approaches the line y = k without touching it--y is almost equal to k, but y is never exactly equal to k.