Determine asymptotes of the following function:

[math]f(x) = \frac{x - 2}{e^{1/x}}[/math]I've managed to find the vertical asymptote [imath]x = 0[/imath], but I'm struggling with oblique one. It's equation is [imath]y = ax + b[/imath] and I calculated that [imath]a = 1[/imath] using formula

[math]a = \lim_{x \to \infty} \frac{f(x)}{x}[/math]Now, I have a problem finding b. I used formula

[math]b = \lim_{x \to \infty} (f(x) - ax)[/math]and got that

[math]b = \lim_{x \to \infty} \bigg(\frac{x - 2}{e^{1/x} } - x\bigg)[/math]which I don't know how to solve.

P.S.

I don't speak English very well and it's my first time asking question here, so sorry if there are some mistakes.

[math]f(x) = \frac{x - 2}{e^{1/x}}[/math]I've managed to find the vertical asymptote [imath]x = 0[/imath], but I'm struggling with oblique one. It's equation is [imath]y = ax + b[/imath] and I calculated that [imath]a = 1[/imath] using formula

[math]a = \lim_{x \to \infty} \frac{f(x)}{x}[/math]Now, I have a problem finding b. I used formula

[math]b = \lim_{x \to \infty} (f(x) - ax)[/math]and got that

[math]b = \lim_{x \to \infty} \bigg(\frac{x - 2}{e^{1/x} } - x\bigg)[/math]which I don't know how to solve.

P.S.

I don't speak English very well and it's my first time asking question here, so sorry if there are some mistakes.

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