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1) I saw in a book that "the limit as $x$ approaches positive infinity of $e^x$ equals $0$" I want to ask about this?

2) if the $a$ is a negative number and we take a limit like "the limit as $x$ approaches positive infinity of $a^x$ equals?" and if $x$ approaches minus infinity then what happens?


Please also tell me what would happen if $a$ is positive number.

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    then my question was if we take any number in place of e and do the the same then what happens, if the number is positive and what happens and if the number is negative2011-10-05

1 Answers 1

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As long as the base is greater than one, the same thing happens. $\lim_{x \to \infty}a^x=\infty, \lim_{x \to -\infty}a^x=0$ for any $a \gt 1$. $\lim_{x \to +\infty}a^x=0, \lim_{x \to -\infty}a^x=\infty$ for any $0 \lt a \lt 1$.

For $a \lt 0$, $a^x$ is undefined in the reals for irrational $x$

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    A nice answer; I note that you don't include the case of a=1 exactly. :)2012-09-01