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Please help me in explaining how to get the following results:

$\lim_{x \rightarrow 0} (x^{-2}-x^{-1}) = \infty$


$\lim_{x \rightarrow \infty} (3^x-2^x) = \infty$

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Thank you (Amzoti) for editing the question. I'm not sure how to activate the Latex arguments the posts – Logarithm Mar 20 '13 at 5:25
You can use L-hospital rule for the first limit and show that the limit tends to infinity. For the second limit you can use the $a^x$ expansion and then use limit on that series. – lsp Mar 20 '13 at 5:29

2 Answers 2

up vote 6 down vote accepted


$$==\;\;\;\;x^{-2}-x^{-1}=\frac{1-x}{x^2}\xrightarrow [x\to 0]{}\ldots$$


Further hint:

$$|q|<1\Longrightarrow q^n\xrightarrow[n\to\infty]{}0$$

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Thank you so much! Mathematics is so beautiful ... – Logarithm Mar 20 '13 at 5:37

$\lim_{x \rightarrow \infty} 3^x(1-(\frac{2}{3})^x)$

now as ${x\rightarrow\infty}$



$3^{x}\rightarrow \infty$

hence the final answer is $\infty$

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