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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Qwynn
Updated on August 01, 2022Comments

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.

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.

Qwynn over 9 yearsAh! Written that way you can see what to do right away! thank you

André Nicolas over 9 yearsYou are welcome. Limits at $0$ make Maclaurin series natural, since these give the behaviour of a function near $0$.


Admin over 9 yearsYou're welcome.