Having trouble with a question on L'Hopital's rule. I have never come across it must have misseda lecture. From what I understand the rule approximates values at a limit. Here's what I have anyway.(adsbygoogle = window.adsbygoogle || []).push({});

I've derived a velocity gradient for a spherically symmetric, isothermal stellar wind as follows.

[tex]\frac{dv}{dr}=\frac{2a^2}{r}(1-\frac{r_c}{r})\frac{v}{(v^2-a^2)} [/tex]

where a is the sound speed and [tex]v=a[/tex] at the critical point [tex]r=r_c[/tex]

So apparently when applying L'Hopital's rule I can approximate the velocity gradient as

[tex](\frac{dv}{dr})_r_c=+or-\frac{a}{r_c}[/tex]

When I apply the limits all I can come up with is the following and I do not understand what Ihave to do to get the quoted answer.

[tex](\frac{dv}{dr})_r_c=\frac{2a^2}{r_c}[/tex]

Thanks in advance.

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# L'Hopital's Rule

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