![plot([sin(`*`(Pi, `*`(x))), ln(x)], x = 0 .. 2, color = [red, blue]); 1](images/LHop_1.gif){kind=small}
MATH 136-02 -- Advanced Placement Calculus
September 30, 2009
To L'Hopital's Rule
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Suppose we want to determine whether
exists or not. This is an
example of an "indeterminate 0/0 form" (like the limits of the difference
quotients that give derivatives). Let's try "zooming in" on the graphs near
= 1, and scale the 
and 
axes the same:
What are we seeing here?
| > | ![plot([sin(`*`(Pi, `*`(x))), ln(x)], x = .5 .. 1.5, color = [red, blue], scaling = constrained); 1](images/LHop_7.gif){kind=small} |
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| > | ![plot([sin(`*`(Pi, `*`(x))), ln(x)], x = .9 .. 1.1, color = [red, blue], scaling = constrained); 1](images/LHop_9.gif){kind=small} |
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