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Article Rating     # Can you divide infinity by 2?

Update: As of September 2022, we have much more interactive ways for you to learn about the foundational concept of Limits at Infinity, making heavy use of Desmos graphing calculators. Please visit our Introduction to Limits at Infinity to start to really get this material down for yourself. It’s all free, and designed to help you do well in your course.

If you just need practice with limits problems for now, previous students have found what’s below super-helpful. And if you have questions, please ask on our Forum!

Summary

To analyze limit at infinity problems with square roots, we’ll use the tools we used earlier to solve limit at infinity problems, PLUS one additional bit: it is crucial to remember [ bbox[yellow,5px] < begintext x &= sqrt \[8px] text x &= -sqrt \[8px] end > ]

• For example, if \$x = 3\$, then \$x = 3 = sqrt<9>\$.
• By contrast, if \$x = -3\$, then \$x = -3 = -sqrt<9>\$.

You must remember that \$x = -sqrt\$ in any problem where \$x to, -infty\$, since you’re then automatically looking at negative values of x. The problems below illustrate, starting with part (b) of the first one.

For a fuller discussion of this crucial point, please visit the screen “Limit at Infinity with Square Roots” in our Limits Chapter devoted to this topic. We also have specifically-designed interactive Desmos graphing calculators there that will help you understand what it is you’re doing when you compute these limits.

Problem #1
Find the requested limits.
(a) \$displaystylefrac>>\$
(b) \$displaystylefrac>>\$
Show/Hide Solution
Solution Summary Solution (a) Detail Solution (b) Detail
(a) \$sqrt\$
(b) \$-sqrt\$

It’s all free: our only aim is to support your learning via our community-supported and ad-free site.

We use our usual “trick” of dividing the numerator and the denominator by the largest term in the denominator, which here is \$x\$. Note that in the last step, we used the fact that \$displaystylefrac = 0>\$.
We can verify the result with a quick look at the graph of the function. Note that the horizontal line \$y = sqrt\$ is a horizontal asymptote for this graph.

Before we do anything else, let’s look at the function and decide whether we expect the limit — if it exists (as it typically will in these problems) — will be positive or negative. We can reason quickly: in \$frac right)>>\$, the numerator will always be positive because of the square root. The denominator, on the other hand, will always be negative, because we’re looking at ever-increasing negative values for x. Hence as \$x to, -infty\$, the fraction will always have a negative value, and so if we find a number as the limit, we expect it to be negative. This quick initial reasoning is a good check to use against our final result.

To obtain that result, we again use our usual “trick” of dividing the numerator and the denominator by the largest term in the denominator, which here is \$x\$.

The crucial part of this solution: since we’re looking at \$x to, -infty\$, we’re interested only in negative values of \$x,\$ and so we’ll use the fact that \$x = -sqrt.\$ [ begin lim_frac> &= lim_frac<-sqrt>> \[8px] &= lim_frac>> \[8px] &= lim_ -sqrt> \[8px] &= -sqrt quad cmark end ] Note that in the last step, we used the fact that \$displaystyle\$. Notice that we obtained a negative number as our answer, which matches our quick initial reasoning above.
We can verify the result with a quick look at the graph of the function. Note that the horizontal line \$y = -sqrt\$ is a horizontal asymptote for this graph.

## What is infinity divided by 2?

And the infinity is such a number that when we divide it by 2,then it remains infinity. The concept around infinity revolves around endlessness. Hence, any “fraction” of infinity is infinite.

## What is the value of 2 by infinity?

If a number is multiplied by infinity, then the value of the product is also equal to infinity.

## What is infinity divided by 3?

Infinity divided by anything that is finite and non-zero is infinity.

## Can infinity be divided?

Never. There are an infinite number of different values for infinity, and some are infinitely larger than others, and some are infinitely smaller than others.

## Is dividing by Infinity zero?

Using L’Hôpital’s rule to evaluate limits of fractions where the denominator tends towards infinity can produce results other than 0. This means that, when using limits to give meaning to division by infinity, the result of «dividing by infinity» does not always equal 0.

## What is 1 divided infinity?

Infinity is not a real number and is only used as a representation for an extremely large real number. Dividing 1 by infinity is equal to zero. In general, any real number divided by infinity is zero, and the quotient of nonzero real numbers that divide infinity is infinity.

## What is 5 divided infinity?

Answer: Evaluate the value of 5 divided by infinity. Hence, 5 divided by infinity is 0. Alternatively, we know that any number divided by 5 is equal to 0.

## Is infinity equal to zero?

In terms of logarithms, the original value 0 corresponds to −∞, while the original infinite value corresponds to +∞. When we treat both possible values −∞ and +∞ as a single infinity, we thus treat the original values 0 and infinity as similar.

## Is 2 times infinity bigger than infinity?

The answer depends on which notion of infinity we use. The infinity of limits has no size concept, and the formula would be false. The infinity of set theory does have a size concept and the formula would be kind of true. Technically, statement 2 ∞ > ∞ is neither true nor false.

## What is the biggest number?

A «googol» is the number 1 followed by 100 zeroes. The biggest number with a name is a «googolplex,» which is the number 1 followed by a googol zeroes.

## Is ∞ a number?

No. Infinity is not a number. Instead, it’s a kind of number. You need infinite numbers to talk about and compare amounts that are unending, but some unending amounts—some infinities—are literally bigger than others.

## Is infinity plus 1 bigger than infinity?

Yet even this relatively modest version of infinity has many bizarre properties, including being so vast that it remains the same, no matter how big a number is added to it (including another infinity). So infinity plus one is still infinity.

## Is half of infinity still infinity?

It’s infinite. One way to look at it is to realize that if you added two finite things together, the answer is finite, so 1/2 of infinity cannot be finite, hence infinite.

## What is the value of 1 ∞?

In fact, it is impossible to divide a number by infinity and get a result of 0. However, this does not mean that the value of 1/infinity is anything other than incredibly small. In practical terms, the value of 1/infinity can be thought of as being equal to zero.

## What is the value of ∞?

Infinity is not a real number, it is an idea. An idea of something without an end. Infinity cannot be measured.

## What is the value of ∞ 0?

Answer: Infinity to the power of zero is equal to one.

## Is infinity times 0 still 0?

Any number times any number is a number, so let’s just call any number 1. Any number times 0 equals 0 and any number times infinity equals infinity. In this way, they are similar to the square root of -1. As long as there are an even number, you get a real number.

## Is infinity bigger than Googolplexian?

Googolplex may well designate the largest number named with a single word, but of course that doesn’t make it the biggest number. In a last-ditch effort to hold onto the hope that there is indeed such a thing as the largest number… Child: Infinity! Nothing is larger than infinity!

## Is Beyond infinity possible?

Not only is the infinity of decimals bigger than that of the counting numbers – there is no biggest infinity. Beyond infinity is another infinity, and beyond that is yet another… and even after you’ve reached an infinity of infinities, there’s still another infinity beyond that.

## What is E to infinity?

e raised to infinity is infinity. When e is raised to the power of infinity, it means that e is increasing at a very rapid rate and is tending toward an extremely large number. This means that e to the power of infinity is also infinity.

## Is there negative infinity?

The symbol “∞”, (called the lemniscate), is used to denote infinity. It looks like a sideways 8. Similarly, there is a concept called negative infinity, which is less than any real number. The symbol “-∞” is used to denote negative infinity.

## Is 1 infinity a thing?

Infinity is a concept, not a number. We know we can approach infinity if we count higher and higher, but we can never actually reach it. As such, the expression 1/infinity is actually undefined.

## What is the answer if 0 is divided by 1?

We can say that zero divided by 1 equals zero and we can also say that this is «defined» as well.

## What is 1 divided by minus infinity?

Answer and Explanation: −1∞ is 0. Any value divided by infinity is 0 except infinity divided by infinity, which is undefined.

## What is sin at infinity?

Also, ∞ is undefined thus, sin(∞) and cos(∞) cannot have exact defined values. However, sin x and cos x are periodic functions having a periodicity of (2π). Thus, the value of sin and cos infinity lies between -1 to 1. There are no exact values defined for them.  