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Calc III Ch13 Notes_Part11

Calc III Ch13 Notes_Part11 - Differentiability In...

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Unformatted text preview: Differentiability: In single—variable functions this was easy. . .did the derivative exist at that point? , @M/WW-S- £7 ,. mu m; ’V EX: Where is f (x): x differentiable? 5V Xfld I’m/é ‘/ 50 . f d/ngffi’é’cr x—4 /:X'LI)*-)((/__.Zlfl—#= 6? M I”??? " (Hf . In multiwariable calculus, this is NOT easy. fix, y). is. differentiable at (a, .b) if A2 can be expressed as A2 =. W ’1. 51‘4" *5-4? . 01:1?me Errors. Where both 51 and 52 —>0 as (Ax,Ay) —> (0, 0). 1/" x o‘y EX: Show that f (x, y) = 4 y2 — x is differentiable everywhere. / M flflw,-—--- A Z = ”WE/Mr) — MW : 4044/) 2’ (/WAX.) "' (/y‘zflx All}??? “4&5 K _— 4174/ my *‘/4/‘6'3’- .4): 74743 7546’“ “at We 52 = 71x +254 { «*— “"0““ C ”A r r 24 my» We,“ — x +5 4 _ at, 4x 78/ +30 fg/Aydy , “050 fa )* z z 67; fill”, ’zflfnf/O /y -X 4—)) (Ahay) Iota: J , 2y \ 5:91" we r. gray +Qx)[email protected])[email protected])@fl «4 r t y if 61 ...
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