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Is 1 to the power of infinity an indeterminate form?
We first learned that 1^infinity is an indeterminate form, meaning that a limit can’t be figured out only by looking at the limits of functions on their own. You’ll then take the limit of the exponents of the e function. And Step 2: Apply L’Hopital’s Rule so you can find your limit.
What is 1 raised to the power of infinity?
One if multiplied by any number of times gives the result 1. Hence 1 raised to the power of infinity is 1.
Is infinity raised to infinity indeterminate?
A limit confirmed to be infinity is not indeterminate since it has been determined to have a specific value (infinity).
Is infinity infinity indeterminate?
But Infinity — Infinity is an indeterminate quantity. If you add any two humongous numbers the sum will be an even larger number. If you add infinity (an impossibly large number) plus another impossible large number the result is still an impossibly large number (infinity). Though infinity – infinity IS indeterminable.
Why is infinity minus infinity indeterminate?
It is impossible for infinity subtracted from infinity to be equal to one and zero. Using this type of math, it would be easier to get infinity minus infinity to equal any real number. Therefore, infinity subtracted from infinity is undefined.
Is infinity determinate or indeterminate?
An undefined expression involving some operation between two quantities is called a determinate form if it evaluates to a single number value or infinity. An undefined expression involving some operation between two quantities is called an indeterminate form if it does not evaluate to a single number value or infinity.
Is infinity over zero indeterminate?
Infinity, negative or positive, over zero will always result in divergence. As well, one over zero has infinite solutions and is therefore not indeterminate. We can determine a universal solution, but an indeterminate answer is one that needs more information.
Why is 1 ∞ an indeterminate form?
(The indeterminacy of ∞ 0 actually follows in the same way, by taking the factors in the other order.) This is just one more consideration 1 ∞ can be roughly rewritten as: Now just think to the zeroth root of 1: every number raised to 0 is one so the zeroth root of 1 could be every number! This is why 1 ∞ is an indeterminate form.
What limits are not indeterminate?
Finally, while limits resulting in zero, infinity, or negative infinity are often indeterminate forms, this is not always true. Infinity, negative or positive, over zero will always result in divergence. As well, one over zero has infinite solutions and is therefore not indeterminate.
What is the indeterminate form of the base function?
In fact, a better notation of this type of indeterminate form should be ( → 1) ∞, where the right arrow means the number 1 is the limit of the base function, not all of the value of the base function is literally 1 (i.e. not the case like lim n → ∞ 1 n ). This is the same when we write other indeterminate form, for example like → 0 → 0.