How could I find a slant asymptote of a function like x*e^(1/x)

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Is there a general way of finding this. Usually what I find on the internet is dividing the function by ax + b but I can't seem to make it work

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Hint: Use differential geometry!

The oblique asymptotes have the equation:

$$y=kx+b, \space \text{ with } \space \space k = \lim_{x \to \infty} \frac{f(x)}{x}, \space \space b = \lim_{x \to \infty} [f(x) - kx].$$