## Can an absolute value be infinity?

The Absolute Infinite (symbol: Ω) is an extension of the idea of infinity proposed by mathematician Georg Cantor. It can be thought of as a number which is bigger than any conceivable or inconceivable quantity, either finite or transfinite.

**What are limits at infinity related to?**

By limits at infinity we mean one of the following two limits. In other words, we are going to be looking at what happens to a function if we let x get very large in either the positive or negative sense. Also, as we’ll soon see, these limits may also have infinity as a value.

### Are there any limits that have infinity as a value?

Also, as we’ll soon see, these limits may also have infinity as a value. 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 → − ∞ .

**When to look for limit of absolute value function?**

Because the argument of an absolute value function may be positive or negative, we have to satisfy both cases: when x > 0 and x < 0. Because we are looking for the limit as x approaches 2, it falls into the first case since 2 > -3/2.

#### How to find the limit of lim X?

lim x → ∞ | x | + 2 4 x + 3 = lim x → ∞ x + 2 4 x + 3. Factor the x out of the numerator and denominator. Then divide out the common factor. Evaluate the limit. Notice that this is the same function as in Example 1, but this time x is becoming negative. Simplify the absolute value.

**Is the proof of the infinite limit the same?**

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.