Yes. In such a case, manipulate the problem so that you get the indeterminate form 0/0 or infinity/infinity, then proceed with l'Hopital's Rule.
Zero times infinity is defined as "indeterminate".
Firstly, infinity is not a number (at least in lower level mathematics). You must instead use the language of limits to describe infinity. Using limits, a function which diverges to infinity multiplied by a function which diverges to infinity has a product which also diverges to infinity. However, taking this product, and subtracting away a function which diverges to infinity is "of indeterminate form". It might converge to zero, it might be diverge to positive infinity, it might diverge to negative infinity, or it might converge to a constant. In order to figure out which one of these possibilities applies, you must get the indeterminate form into the form infinity divided by infinity or 0/0 and then apply L'Hospital's rule. Edit: Just a pet peeve of mine. It's L'Hôpital, not L'Hospital. Even textbooks don't spell it right.
Because it does
Infinity/2,000,000,000,000,000 is the simplest form.
Yes. In such a case, manipulate the problem so that you get the indeterminate form 0/0 or infinity/infinity, then proceed with l'Hopital's Rule.
It's indeterminate.
Zero times infinity is defined as "indeterminate".
Infinity added to anything is infinity (with the exception of -infinity, as it is an indeterminate form). Thus, infinity + 2 = infinity.The problem is that (although it is easy to think of it this way) infinity is not a number. Infinity is, rather, the concept that something is boundless.Thus, "infinity + 2" is a category error. (This is (supposed to be) a sum in maths, and infinity is not a number.)
Firstly, infinity is not a number (at least in lower level mathematics). You must instead use the language of limits to describe infinity. Using limits, a function which diverges to infinity multiplied by a function which diverges to infinity has a product which also diverges to infinity. However, taking this product, and subtracting away a function which diverges to infinity is "of indeterminate form". It might converge to zero, it might be diverge to positive infinity, it might diverge to negative infinity, or it might converge to a constant. In order to figure out which one of these possibilities applies, you must get the indeterminate form into the form infinity divided by infinity or 0/0 and then apply L'Hospital's rule. Edit: Just a pet peeve of mine. It's L'Hôpital, not L'Hospital. Even textbooks don't spell it right.
Yes. The rule is used to find the limit of functions which are an indeterminate form; that is, the limit would involve either 0/0, infinity/infinity, 0 x infinity, 1 to the power of infinity, zero or infinity to the power of zero, or infinity minus infinity. So while it is not used on all functions, it is used for many.
Oh, what a lovely question! When you divide infinity by infinity, you're entering a realm of endless possibilities and wonder. In mathematics, this expression is considered indeterminate because infinity is not a fixed number. Embrace the beauty of the unknown and continue exploring the infinite canvas of mathematics with joy and curiosity.
Because it does
infinity = '∞'
Infinity/2,000,000,000,000,000 is the simplest form.
There is no number greater than infinity. Infinity is defined to be greater than any number, so there can not be two numbers, both infinity, that are different.However, when dealing with limits, one can approach a non-infinite value for a function involving infinity. Take, for example, 2x divided by x, when x is infinity. That value is indeterminate, because infinity divided by infinity is defined as indeterminate, and 2 times infinity is still infinity.But, if you look at the limit of 2x divided by x, as x approaches infinity, you do get a value, and that value is 2. This does not mean that 2x when x is infinity is twice infinity, it just means that, right before x becomes infinity, the ratio is right before 2.Infinity should not be thought of as a number, but rather as a direction. Whereas a number represents a specific quantity, infinity does not define given quantity. (If you started counting really fast for billions of years, you would never get to infinity.) There are, however, different "sizes of infinity." Aleph-null, for example, is the infinity that describes the size of the natural numbers (0,1,2,3,4....) The infinity that describes the size of the real numbers is much larger than aleph-null, for between any two natural numbers, there are infinite real numbers.Anyway, to improve upon the answer above, it is not meaningful to say "when x is infinity," because, as explained above, no number can "be" infinity. A number can approach infinity, that is to say, get larger and larger and larger, but it will never get there. Because infinity is not a number, there is no point in asking what number is more than infinity.
Indeterminate since we are not given the time units to compute the rate, which is in the form change in quantity / time.