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Calc III Ch13 Notes_Part12

Calc III Ch13 Notes_Part12 - Theorem If f(x y is...

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Unformatted text preview: Theorem: If f(x, y) is differentiable at (a, b), then it is continuous at (a, b). NOTE: Like in calc 1, this is more useful in the contrapositive. . . fl/yf (an/WM :—> ”57- A’FW . In Cale l, we simply looked at the derivative to see if it existed at a point. But unfortunately in multi-variable calculus. . . ****It is possible to have a function in which both partials exist at a point, but is NOT differentiable at that point. **** Ex #46 /:{ylV/ 5% [WM/3 , X\)/#(C}a) 0W 0 @(mx Md) ( ”ml/fit;- 5/};— Zm‘ J/(m/ 0!; éfly/Z’) fififidx’): 69/ .. 0 4""0 (AKfiM’ , G / :[mf //”/J*4:):/(’kd/ 4 X y 4X’70 4/ {Zn/WM) ' O rail/3: 0 *‘(4‘0’ : 0 Bow PfirflMfi EXHT. AX games My W N7)!“ D/FEMM/Mlg Z/VW pl :— gfl/b/VE :7 /V//"’ (”W/W5 :) fldf 0/F/‘7/(M74fl XIV / ...
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