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

I don't know if the following is valid, so I'll appreciate if someone could tell me if it's ok. I want to find

[tex] \lim_{x\rightarrow \infty} \frac{x}{\sqrt{a^2+x^2}} [/tex]

2. Relevant equations

3. The attempt at a solution

Using L'Hopital rule doesn't appear to help, because repeatedly differentiating both the top and bottom gives the same limit. So I did a substitution:

[tex]x=a \tan \theta[/tex]

And the problem now becomes [tex]\lim_{\theta \rightarrow \frac{\pi}{2}} \sin \theta [/tex] which easily evaluates to 1. Is this correct?

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# Homework Help: Valid method of evaluating limit?

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