It IS indeterminate.
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.
Yes, infinity over zero is considered an indeterminate form. This is because while the numerator approaches infinity, the denominator approaches zero, leading to a situation where the expression does not have a well-defined limit. Depending on the context of the limit, the result can vary significantly, making it indeterminate rather than a fixed value.
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.
The value of anything raised to the power of infinity depends on the base. If the base is greater than 1, the value approaches infinity. If the base is equal to 1, the value remains 1. If the base is between 0 and 1, the value approaches 0. If the base is 0, the expression is typically considered to be 0, but if it's 0 raised to the power of infinity, it is an indeterminate 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.
Yes, infinity over zero is considered an indeterminate form. This is because while the numerator approaches infinity, the denominator approaches zero, leading to a situation where the expression does not have a well-defined limit. Depending on the context of the limit, the result can vary significantly, making it indeterminate rather than a fixed value.
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.
The value of anything raised to the power of infinity depends on the base. If the base is greater than 1, the value approaches infinity. If the base is equal to 1, the value remains 1. If the base is between 0 and 1, the value approaches 0. If the base is 0, the expression is typically considered to be 0, but if it's 0 raised to the power of infinity, it is an indeterminate form.
Because it does
infinity = '∞'
Infinity/2,000,000,000,000,000 is the simplest form.