Differential Theorems
Rolle's Theorem
If
exists in interval 
and 
, then there is a value 
for which 
holds true.Mean-value Theorem
If
exists in interval 
, then there is a value 
for which 
holds true.L'Hospital's Theorem
Let
be differentiable near 
, and 
and 
.If
exists, then 
Taylor's Theorem
If
is differentiable 
times in an interval including 
, then there is a value 
that satisfies
exists between 
and 
).Maclaurin's Theorem
If
is differentiable 
times in an interval including 0, then there is a value 
that satisfies
exists between 0 and 
).Taylor series/Maclaurin series
When
is differentiable an infinite number of times and
Example of Maclaurin series
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