L'Hopital's Rule

Test Preparation AP Test Preparation
1

<p>Can someone explain how to find the following two limits solely through analytic means?</p>

<p>lim x ln x
x–>0+</p>

<p>lim x tan (1/x)
x–>Infinity</p>

2

<p>For the first one, rewrite it as ln x / (1/x).</p>

<p>using L’Hopital’s rule, you know that it equals the limit of (1/x)/(-1/x^2)
=lim -x
=0</p>

<p>I don’t feel like figuring out the second one right now, but there’s a start, at least.</p>

3

<p>lim xtan(1/x)= lim tan(1/x)/(1/x)</p>

<p>Put y=(1/x) the y—>0</p>

<p>lim tany/ y=0 (fROM sANDWICH THEOREM)
y->0</p>