Prove the given theorem and provide (1) examples. Theorem 1.9 (Taylor's series for a function of several varlables) f(x+Ax,X + Axz.....X + Ax) af Ax, +...+ Ax, + (Ax) +... + af af -AXn 1,af af Ax,Axz +.. = f(x1,X2,...Xn) + -Ax, + Exeixe,+ ("xg)e af Axn-14x +... "xel-"xe +2

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Chapter2: Second-order Linear Odes
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Prove the given theorem and provide (1) examples.
Theorem 1.9 (Taylor's series for a function of several variables)
f(x + 4x1, X; + Ax2.....X + Axn)
1, af
af
Ax +
ax
Ax,Axz +
af
= f(x1, X2,..Xn) +
af
Ax2
Ax, +
ax2
+ 2
Axn-14x] +...
"xet-"xe
Transcribed Image Text:Prove the given theorem and provide (1) examples. Theorem 1.9 (Taylor's series for a function of several variables) f(x + 4x1, X; + Ax2.....X + Axn) 1, af af Ax + ax Ax,Axz + af = f(x1, X2,..Xn) + af Ax2 Ax, + ax2 + 2 Axn-14x] +... "xet-"xe
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