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Maged Saeed
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why $$1^\infty$$ is indeterminate form?
1 raised to any finite power is 1, of course, but some limits are of this indeterminate form, and have a limit that isn't equal to 1.Maged Saeed said:why $$1^\infty$$ is indeterminate form?
Maged Saeed said:why $$1^\infty$$ is indeterminate form?
PeroK said:Anything with ##\infty## is an indeterminate form, because ##\infty## is not a number.
I agree. It's not indeterminate because you can determine what the limit will be.Mentallic said:I don't believe that [itex]1/\infty[/itex] is an indeterminate form because its value cannot be anything other than 0.
That's not true. While ##[\infty - \infty]## and ##[\frac{\infty}{\infty}]## are indeterminate forms, ##[\infty + \infty]## and ##[\infty * \infty]## are not considered indeterminate.PeroK said:Anything with ##\infty## is an indeterminate form, because ##\infty## is not a number.
Mark44 said:That's not true. While ##[\infty - \infty]## and ##[\frac{\infty}{\infty}]## are indeterminate forms, ##[\infty + \infty]## and ##[\infty * \infty]## are not considered indeterminate.
Mark44 said:I agree. It's not indeterminate because you can determine what the limit will be.
No, it is not indeterminate. If the numerator approaches 0 and the denominator becomes unbounded, the limit is 0.Maged Saeed said:Me too .
How about
$$\frac{0}{\infty}$$
Is it indeterminate too?
I think so
An indeterminate form is a mathematical expression in which the limit cannot be determined without further analysis. This typically occurs when the expression includes a variable that approaches a certain value, but the outcome of the expression is unclear.
To solve an indeterminate form, you must use mathematical techniques such as L'Hopital's rule or algebraic manipulation. These methods help to simplify the expression and determine the limit.
There are six types of indeterminate forms: 0/0, ∞/∞, 0*∞, ∞-∞, 0^0, and ∞^0. Each type has its own unique properties and requires different methods to solve.
Indeterminate forms are important in calculus because they represent situations where the limit of a function cannot be determined by simply plugging in values. These forms require a deeper understanding of the function and its behavior to determine the limit.
No, not all indeterminate forms can be solved. Some forms may have infinite limits or no limit at all. In these cases, it is important to understand the behavior of the function and determine the limit using other methods such as graphing or numerical approximation.