Taylor Series Expansion
2016+Week4
2016+Week4
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Second Partial Derivatives<br />
hk<br />
k<br />
y<br />
h<br />
x<br />
F<br />
k<br />
y<br />
h<br />
x<br />
F<br />
k<br />
y<br />
h<br />
x<br />
F<br />
k<br />
y<br />
h<br />
x<br />
F<br />
x<br />
f<br />
y<br />
x<br />
y<br />
f<br />
y<br />
x<br />
f xy 4<br />
)<br />
,<br />
(<br />
)<br />
,<br />
(<br />
)<br />
,<br />
(<br />
)<br />
,<br />
(<br />
)<br />
,<br />
(<br />
2<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
2<br />
2<br />
2<br />
)<br />
,<br />
(<br />
)<br />
,<br />
(<br />
2<br />
)<br />
,<br />
(<br />
)<br />
,<br />
(<br />
h<br />
y<br />
h<br />
x<br />
F<br />
y<br />
x<br />
f<br />
y<br />
h<br />
x<br />
F<br />
x<br />
f<br />
x<br />
x<br />
f<br />
y<br />
x<br />
f xx<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
2<br />
2<br />
2<br />
)<br />
,<br />
(<br />
)<br />
,<br />
(<br />
2<br />
)<br />
,<br />
(<br />
)<br />
,<br />
(<br />
k<br />
k<br />
y<br />
x<br />
F<br />
y<br />
x<br />
f<br />
k<br />
y<br />
x<br />
F<br />
y<br />
f<br />
y<br />
y<br />
f<br />
y<br />
x<br />
f yy<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
Following formulas can be verified by taking the limits<br />
and<br />
0<br />
h 0<br />
<br />
k