(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

1. Find the limit of [tex]\lim_{x\rightarrow 0} \frac{1}{xe^{\frac{1}{x}}}[/tex]

2. " " " " [tex]\lim_{x\rightarrow\infty} \frac {x}{\log_e x}[/tex]

2. Relevant equations

[tex]\lim_{x\rightarrow\infty} \frac{N}{x} = 0[/tex]

[tex]\lim_{x\rightarrow n} x+a = \lim_{x\rightarrow n} x + \lim_{x\rightarrow n} a[/tex] etc

3. The attempt at a solution

1. I put in values of x close to 0, and as I approached from above I got values very close to 0, but when I approached from below the numbers became massively large and negative ([tex]f(-0.1)=-220264, f(-0.01)=-2.688\times10^{45}[/tex]). The answer in my book is zero, but my numbers say there is no limit as values of x approaching 0 do not approach the same number. Have I missed something out or is the book wrong?

2. In the book the answer is "no limit", but I can't think of a way to evaluate it to prove it. The only thing I've thought of is dividing by x, but that did nothing and ended up going in circles :/

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# Homework Help: 2 finding limits problems

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