Use series to evaluate limit
2,734
We have
$$3x^2(e^{-2/x^2}-1)=3x^2\left(1-\frac{2}{x^2}+O\left(\frac1{x^4}\right)-1\right)=-6+O\left(\frac1{x^2}\right)\xrightarrow{x\to\infty}-6$$
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Author by
Qwynn
Updated on August 01, 2022Comments
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Qwynn over 1 year
limit as x approach infinity of $3(x^2)(e^{-2/x^2}-1)$. I don't know what series to use.
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André Nicolas over 9 yearsLet $x^2=\frac{1}{t}$. So we are interested in $\frac{3}{t}(e^{-2t}-1)$. Use the familiar Maclaurin expansion.
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Qwynn over 9 yearsAh! Written that way you can see what to do right away! thank you
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André Nicolas over 9 yearsYou are welcome. Limits at $0$ make Maclaurin series natural, since these give the behaviour of a function near $0$.
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Admin over 9 yearsYou're welcome.
