Help finding "values" for things containing infinity.?

What is:

1. inf^1

2. pi^inf

3. 1^ -inf

I need to know if they are indeterminate, determinate ( and give a value), or if they don't exist. Please and thanks,

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  • 1 decade ago
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    1^(-infinity) is an indeterminate form. This means that we cannot infer the limit of A^B if we are only given that the limit of A is 1 and the limit of B is negative infinity. For example, as n approaches negative infinity, the limit of 1^n is 1, but the limit of (1+1/n)^n is e.

    The other two forms are determinate. If lim A = infinity and lim B = 1 then lim A^B = infinity. Likewise if lim A = pi and lim B = infinity then lim A^B = infinity.

    There are only seven indeterminate forms: inf - inf, 0 * inf, 0/0, inf/inf, 0^0, inf^0, and 1^inf. Note that 1^(-inf) is just the "reciprocal" of 1^inf.

    NOTE TO OTHER RESPONDERS: This is a calculus question. Please do not respond unless you have studied calculus.

  • 1 decade ago

    1) ∞

    anyting to the 1 is just itself

    2) π^∞

    indeterminate, its too huge.

    3) 1^-∞ = 1

    You can multiply 1 by itself as many times as you want it will still be 1, the negative just makes it a reciprocal, but the reciprocal of 1 is 1.

  • 1 decade ago

    1: Any number raised to the power one is unchanged ie.

    0^1 = 0

    1^1 = 1

    2^1 = 2

    2: anything other than 0 raised to the power of infinity is itself infinite

    3: 1 raised to the power of anything stays 1

    I know this doesn't answer your question entirely, but seeing as it's your math homework you really need to be doing some of the work yourself ;)

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