- #1

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lim(a^x_n)^x'_n, when n->infinity = (a^lim x_n)^lim x'_n , n-> infinity,

what i am asking here is if we can go from the first to the second??? or if these two expressions are equal??

any help??

- Thread starter sutupidmath
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- #1

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lim(a^x_n)^x'_n, when n->infinity = (a^lim x_n)^lim x'_n , n-> infinity,

what i am asking here is if we can go from the first to the second??? or if these two expressions are equal??

any help??

- #2

HallsofIvy

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Yes, because the exponential function, a^{x}, is continuous.

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- #4

HallsofIvy

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[tex]\lim_{n \rightarrow \infnty} f(x_n)= f(\lim_{n\rightarrow \infty} x_n)= f(a)[/tex]

- #5

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_{n}is a sequence of numbers converging to a and f is a function continuous at a, then

[tex]\lim_{n \rightarrow \infnty} f(x_n)= f(\lim_{n\rightarrow \infty} x_n)= f(a)[/tex]

yeah this is what i am asking. But what i want to know is if there is a theorem that states this, what you wrote. Or how do we know that this is so?

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Maybe the squeeze theorem?

glenn

glenn

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[tex]\lim_{y \rightarrow x} f(y) = f(x)[/tex]

(ie. the limit exists and is equal to f(x))

- #8

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[tex]\lim_{y \rightarrow x} f(y) = f(x)[/tex]

(ie. the limit exists and is equal to f(x))

Yeah, i know the definition of continuity, i was just wondering if there is a specific theorem that states this, as i have not encountered one on my calculus book. However, i do understand it now.

Many thanks to all of you.

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