Quick Answer: Why Is 1 To The Power Infinity Indeterminate?

Can you use L Hopital’s rule for 1 0?

So, L’Hospital’s Rule tells us that if we have an indeterminate form 0/0 or ∞/∞ all we need to do is differentiate the numerator and differentiate the denominator and then take the limit..

What is E infinity?

e^ ∞ =( 2.71…) ^ ∞ = a constant number multiplied infinite times. = infinity. When e is raised to power infinity,it means e is increasing at a very high rate and hence it is tending towards a very large number and hence we say that e raised to the power infinity is infinity.

What is 1 to the infinity power?

1 raised to power infinity is always 1. If one considers LHL, x will tend to 1 (from left side of 1 on the number line) but will always be less than 1, and raising infinity on something which is less than one will approach to ZERO.

Why is raised to infinity indeterminate?

In the context of real and complex numbers, 1^∞ is undefined, simply because the exponent is not a number. One can have limits of the form x^y, whose value depends on how x goes to 1 as y becomes arbitrarily large. However, the question is not expressed in terms of limits. … 1 raised to the power infinity is not defined.

Is infinity a real number?

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 Infinity Power Infinity?

Infinity is one the paradoxes proposed by Zeno of Elea. Infinity itself doesn’t contain a value but portrays a value of a specific requirement countless number of times. Therefore any mathematical operation on Infinity yields infinity, since it has no specific value. Hence your answer is: Infinity.

Is 1 times infinity an indeterminate form?

This “1∞” (in regards to indeterminate forms) actually means: when there is an expression that approaches 1 and then it is raised to the power of an expression that approaches infinity we can’t determine what happens in that form. Hence, indeterminate form.

Is 0 to the infinity indeterminate?

Now according to question if you multiply zero(exact not as in case of limits) a large no. of times it will always result in zero. So yes zero to power infinity is zero. … 1^ infinity is also indeterminate form.

Is LN Infinity Infinity?

The answer is ∞ . The natural log function is strictly increasing, therefore it is always growing albeit slowly. The derivative is y’=1x so it is never 0 and always positive.

Why is 0 to the power indeterminate?

When calculus books state that 00 is an indeterminate form, they mean that there are functions f(x) and g(x) such that f(x) approaches 0 and g(x) approaches 0 as x approaches 0, and that one must evaluate the limit of [f(x)]g(x) as x approaches 0. In fact, 00 = 1! …

What is negative infinity minus infinity?

If you remove all of the odd numbers from the list of whole numbers, you’re left with the series of all even numbers, which is also endless. So infinity minus infinity is still infinity (at least, if you pick these particular infinite series).

What is the value of 1 minus infinity?

For example, 1 infinity minus infinity could be zero (although, since you can’t measure infinity, how could you be sure).

Whats infinity divided by infinity?

This equation is obvious incorrect. Therefore, infinity divided by infinity is NOT equal to one. Instead we can get any real number to equal to one when we assume infinity divided by infinity is equal to one, so infinity divided by infinity is undefined.

What is 2 to the power infinity?

And here we can prove it as follows.. Here look the infinity means a very very large quantity that means unreachable quantity so simply, {something}^infinity= a very very large quantity(unreachable) that means infinity. So clearly 2^infinity=infinity.