Why Is 1 To The Power Infinity Indeterminate?

Is 0 divided by infinity indeterminate?

Thus as x gets close to a, 0 < f(x)/g(x) < f(x).

Thus f(x)/g(x) must also approach zero as x approaches a.

If this is what you mean by “dividing zero by infinity” then it is not indeterminate, it is zero..

Does Infinity go into the negatives?

Infinity is just a symbol, like 3, denoting an unaccountably large set, so asking if infinity has a beginning doesn’t apply. No, in common use it does not generally include negatives. BUT you can have either a negative or a positive infinity, or an infinity that is both.

Can you do infinity times infinity?

11 Answers. The problem is that the laws of addition and multiplication you are using hold for natural numbers, but infinity is not a natural number, so these laws do not apply. If they did, you could use a similar argument that multiplying anything by infinity, no matter how small, gives infinity, thus ∞×0=∞.

Is 1 divided by infinity?

Infinity is a concept, not a number; therefore, the expression 1/infinity is actually undefined. In mathematics, a limit of a function occurs when x gets larger and larger as it approaches infinity, and 1/x gets smaller and smaller as it approaches zero.

Why is infinity to the zero power indeterminate?

There is no universal value for ∞0. It is indeterminate, and the value depends on how you are getting the ∞ and the 0. … As for your actual question, ∑∞i=1k1/k is infinite since you are adding a non-zero constant (k1/k) to itself an infinite number of times.

What is a constant times infinity?

If anything is multiplied by infinity,then answer is always undefined.

What is infinity divided by 1?

However, 1 divided by ∞ does equal a limit approaching 0. In other words, 1 divided by ∞ does not equal a number or is undefined. As a result, we reached a dead end. Therefore, infinity divided by infinity is still undefined.

Why is 1 to the power of infinity undefined?

If we look at the graph of 1^x, it’s not a straight line, but actually a curve with an asymptote at x=infinity. … Since the asymptote is a line that a curve gets infinitely close to, but never reaches, the function can never reach a real value at x=infinity. Hence, we say it is undefined.

Is 1 to the Power Infinity defined?

In layman terms: as log anything to the base 1 is infinity so we can conclude that 1 to the power infinity won’t necessarily be one but can be anything so that is why 1 to the power infinity is not defined. One if multiplied by any number of times gives the result 1. Hence 1 raised to the power of infinity is 1.

Is 0 to the power of infinity indeterminate?

No, it is zero. Consider the function f(x,y)=xy and consider any sequences {(x0,y0),(x1,y1),…} with xi→0 and yi→∞.

What is infinity minus infinity?

It is impossible for infinity subtracted from infinity to be equal to one and zero. Using this type of math, we can get infinity minus infinity to equal any real number. Therefore, infinity subtracted from infinity is undefined.

Is Infinity equal to zero?

The concept of zero and that of infinity are linked, but, obviously, zero is not infinity. Rather, if we have N / Z, with any positive N, the quotient grows without limit as Z approaches 0. Hence we readily say that N / 0 is infinite. … So we say that 0/0=0, even though we cannot justify the arbitrary change in rules.

What is 1 infinity squared?

similarly , lim(1/x^2) will be 0 , when x tends to infinity. This is not 0 but is close to 0. Infinity is an undetermined or undefined value, it can very big and dividing 1 by that number will result to the value close to 0.

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 negative infinity over infinity indeterminate?

Originally Answered: Can you apply L’hopital’s rule for a negative infinity / infinity case? Yes, because the negative sign is just the constant -1. Bring it out of the limit, and apply L’hôpital’s rule. So you can apply L’hôpital’s rule.

Can zero be divided by 1?

Answer: Zero divided by 1 is 0.

What infinity means?

Infinity, the concept of something that is unlimited, endless, without bound. … The common symbol for infinity, ∞, was invented by the English mathematician John Wallis in 1655.