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kbaumen
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I'm just curious, why, when solving limits, is [itex]1^\infty[/itex] considered an indeterminate form? Isn't 1 raised to any power equal to 1? Why isn't it so simple?
╔(σ_σ)╝ said:Well that is a very good question but the problem is that it depends on how fast your function is going to 1 or infinity.
Your function can be going so slowly to 1, in which case the limit goes to 0.
It`s the same as the undetermined form 0/0 the function on top and bottom could approach zero at the same speed and the limit could go to 1.
kbaumen said:Ah, yes, the function never actually reaches the value [itex]1^\infty[/itex], since we never consider the function at exatcly [itex]x=a[/itex], we are just curious about what it does around that point.
Thank you for your answers.
An indeterminate form in limits is a mathematical expression that cannot be evaluated as a definite number because it involves an operation of "undefined" or "infinite" values. It is often represented by the symbols "0/0" or "∞/∞" and requires further manipulation or use of other mathematical concepts to find its limit.
To determine the limit of an indeterminate form, you can use various mathematical techniques such as L'Hopital's rule, factoring, or substitution. These methods help to simplify the expression and eliminate the "undefined" or "infinite" values, allowing you to find the limit of the function.
Determinate forms are mathematical expressions that can be evaluated to a definite value, while indeterminate forms cannot. In other words, determinate forms have a clear and defined answer, whereas indeterminate forms require further analysis and manipulation to find their limit.
No, not all limits can be evaluated using indeterminate forms. There are certain limits, such as those involving oscillating functions, that cannot be evaluated using the standard techniques for indeterminate forms. In these cases, other mathematical concepts or methods may need to be applied to find the limit.
Indeterminate forms are important in calculus because they allow us to evaluate limits of functions that would otherwise be impossible to determine. They also help us understand the behavior of functions at certain points and can be used to solve real-world problems involving rates of change and optimization.