2B,dd   1Courier New1Symbol New1Courier New1Courier NewTimes New RomanTimes New Roman1Courier New1Courier New1Courier New1Courier NewtPtPtPtP{ d< p {SC&)? U2”?02S$*@$}?^@8 `eQ6#@??? vG}a*p^@|?5^|?5^|?5^0C-@|?5^@==N@033333??@^ߛOw?HzG???b :@RB B@@?@ @@@B ?@@-2??@22$@@(\(\أp= ף(\@(\@HzG@e,?e,? ٹe,?@e,?@0X#ܬ@̴еԶطܸH wk௣x\f(x,y) z = f(x,y)O0O52??@$$$2ho?h2??zG(\?PeB׳@???(\?(\PeB׳@Ќԍ؎܏(r4c0abf(a,b)(x,y,z) = (a,b,f(a,b))42??@$$$??`f8P""(?&+@???H8? <3p@4pD5pH6pL7pP8pT9p^p3abf(a,b) a-fx(a,b)3seg (a,b,f(a,b)) to (a-fx(a,b),b-fy(a,b),f(a,b)+1) b-fy(a,b) f(a,b)+142???$$$??(y-x(\І:Ə?(\????H8?||}~,s0t4up 0Rab0 a+fx(a,b)'seg (a,b,0) to (a+fx(a,b),b+fy(a,b),0) b+fy(a,b)0-2??h!h!@$$$@@أp= أp= Bwf@أp= @أp= @Gl@e,?e,?0fC0-e,?@e,?@0{:s3@X:p\3(q|T < |)!f(a,b)+fx(a,b)(x-a)+fy(a,b)(y-b)%z = f(a,b)+fx(a,b)(x-a)+fy(a,b)(y-b)xyz(\?(\HXT@??00?H`_o!+@@@@@@@@@@@@@@@@@@@@@@@@@@@@   SQRT(16-X^2-Y^2)0 tJFT (-X)/SQRT(16-X^2-Y^2),3.142,0.577)FX (-Y)/SQRT(16-X^2-Y^2)FYThe Red Vector is the 2D GradientR@@Jz|@Kۗ@Times New Roman `The Purple Vector is the3D Gradients&3L @KL<|@Ngq@Times New Roman f(x,y) = sqrt(16-x^2-y^2) Gradient  /1? H̔Y@Xѥ@?@Times New Romanz = f(x,y),*# ,j&@g;@,*#? A(x,y,z) = (a,b,f(a,b)) 3d"r5?ؘYCe̓h58@ seg (a,b,f(a,b)) to (a-fx(a,b),b-fy(a,b),f(a,b)+1)@h^nSx?,`F`|K@` seg (a,b,0) to (a+fx(a,b),b+fy(a,b),0)@h^nH]W@ Tix2]8׏@ z = f(a,b)+fx(a,b)(x-a)+fy(a,b)(y-b)0jP@h^n+@  T딇yk@ahwX