(infinity)^infinity type of limits

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SUMMARY

The discussion focuses on the evaluation of limits of the form (infinity)(infinity), specifically highlighting the limit example \lim_{n \to \infty} n^n = \infty. Participants clarify that this type of limit is straightforward, as both the base and exponent increase without bound, leading to the expression approaching infinity. The conversation contrasts this with more complex indeterminate forms like [1]^{\infty}, which require different techniques for evaluation.

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phymatter
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does anyone know a general way to deal with (infinity)(infinity) type of limits !
pl. help!
 
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phymatter said:
does anyone know a general way to deal with (infinity)(infinity) type of limits !
pl. help!
An example of this type of limit is [tex]\lim_{n \to \infty} n^n = \infty[/tex]

As the base gets larger, and the exponent gets larger, the whole expression gets large without bound (i.e., approaches infinity). There's really nothing tricky about this type of limit, as opposed to one of the indeterminate forms, such as [tex][1]^{\infty}[/tex].
 

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