## What is the limit of something over infinity?

zero

A number over infinity, the answer is zero.

## When can a limit not exist?

Limits & Graphs Here are the rules: If the graph has a gap at the x value c, then the two-sided limit at that point will not exist. If the graph has a vertical asymptote and one side of the asymptote goes toward infinity and the other goes toward negative infinity, then the limit does not exist.

**Is it possible to multiply by infinity?**

Multiplication is an operation defined on real numbers. If you have two real numbers, x and y, you can calculate x⋅y which is a real number. ∞ is not a real number and you cannot multiply with it.

**Does limit exist at a hole?**

If there is a hole in the graph at the value that x is approaching, with no other point for a different value of the function, then the limit does still exist.

### What is the limit at infinity of x > n?

Let N = 1 ε. Therefore, for all x > N, we have |2 + 1 x − 2| = |1 x| = 1 x < 1 N = ε. Use the formal definition of limit at infinity to prove that lim x → ∞(3 − 1 x2) = 3. We now turn our attention to a more precise definition for an infinite limit at infinity.

### What is the set of facts from the infinite limit?

First, let’s note that the set of Facts from the Infinite Limit section also hold if we replace the lim x→c lim x → c with lim x→∞ lim x → ∞ or lim x→−∞ lim x → − ∞ . The proof of this is nearly identical to the proof of the original set of facts with only minor modifications to handle the change in the limit and so is left to you.

**How do you prove an infinite limit at infinity?**

Use the formal definition of limit at infinity to prove that lim x → ∞(3 − 1 x2) = 3. We now turn our attention to a more precise definition for an infinite limit at infinity. for all x > N (see Figure 4.49 ). Similarly we can define limits as x → −∞.

**What is the limit of the number-1?**

In this case we might be tempted to say that the limit is infinity (because of the infinity in the numerator), zero (because of the infinity in the denominator) or -1 (because something divided by itself is one).