Is 0 over infinity an indeterminate form?
0 < f(x)/g(x) < f(x). Hence f(x)/g(x) gets squeezed between 0 and f(x), and f(x) is approaching zero. 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.
Is anything over 0 an indeterminate form?
This is not an indeterminate form, because it’s clear what happens. If f(x) approaches 0 from above, then the limit of p(x)f(x) is infinity. If f(x) approaches 0 from below, then the limit of p(x)f(x) is negative infinity.
Why is 0 times infinity an indeterminate form?
Zero is so small that it makes everyone vanish, but infinite is so huge that it makes everyone infinite after multiplication. In particular, infinity is the same thing as “1 over 0”, so “zero times infinity” is the same thing as “zero over zero”, which is an indeterminate form.
Is infinity to the power of 0 indeterminate?
Answer: Infinity to the power of zero is equal to one. Let’s understand the solution in detail. Explanation: ∞0 is an indeterminate form, that is, the value can’t be determined exactly.
What is indeterminate and undefined?
The big difference between undefined and indeterminate is the relationship between zero and infinity. When something is undefined, this means that there are no solutions. However, when something in indeterminate, this means that there are infinitely many solutions to the question.
What is infinity raised to infinity?
Infinity Plus Infinity Adding infinity to infinity results in infinity.
What is over infinity?
A number, you’re done. A number over zero or infinity over zero, the answer is infinity. A number over infinity, the answer is zero. 0/0 or ∞/∞, use L’Hôpital’s Rule.
Why is infinity minus infinity not zero?
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.
Why is infinity infinity indeterminate?
Since the size of infinity is unknown, we cannot determine any of these situations and therefore the answer is Indeterminate. One reason the answer is indeterminate is because you can find sequences xn,yn of real numbers such that xn,yn→∞ and (xn−yn) can converge to any real value or ±∞.
Is it possible to make infinity / 0 an indeterminate form?
One says definitively, that infinity/0 is “not” possible. Another states that infinity/0 is one of the indeterminate forms having a large range of different values. The last reasons that infinity/0 “is” equal to infinity, ie: Suppose you set x=0/0 and then multiply both sides by 0.
Which is an indeterminate form with a large range of values?
Another states that infinity/0 is one of the indeterminate forms having a large range of different values. The last reasons that infinity/0 “is” equal to infinity, ie: Suppose you set x=0/0 and then multiply both sides by 0. Then (0 x)=0 is true for most any x– indeterminant. Now set x= infinity/0.
When does substituting limit result in indeterminate form?
Substituting a limit that results in a zero, infinity, negative infinity, or any combination of these may result in an indeterminate form. When both functions approach the given limit that results in the indeterminate form, there is not enough information to determine what the behavior of the function is at that point.
What makes an indeterminate form easy to solve?
An indeterminate form is a limit that is still easy to solve. It only means that in its current form as a limit put into a function, it presents too many unknowable characteristics to form an appropriate answer properly. You can’t just solve for the quotient. When solving for a limit, we are looking at two functions so that they make a ratio.