写出下列曲面上点 [tex=1.357x1.214]nVlWDiaq/AF5IB+/Nxj18A==[/tex] 的切平面和法线方程：[tex=11.143x1.214]2yicnz51cy8jm4ENtDpb5yIQqXn1kSX+nCVMXicv4Oc=[/tex] ; 在点 [tex=4.5x1.357]C35jD6PW5IVWpNh1R6XvvSWd42HOSXMvfc/ZubwLlyAgwvUwXNFXUD58ZC8dWa8s[/tex]

2022-06-05

写出下列曲面上点 [tex=1.357x1.214]nVlWDiaq/AF5IB+/Nxj18A==[/tex] 的切平面和法线方程：[tex=11.143x1.214]2yicnz51cy8jm4ENtDpb5yIQqXn1kSX+nCVMXicv4Oc=[/tex] ; 在点 [tex=4.5x1.357]C35jD6PW5IVWpNh1R6XvvSWd42HOSXMvfc/ZubwLlyAgwvUwXNFXUD58ZC8dWa8s[/tex]

答案：

解[tex=40.0x4.357]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[/tex]于是,切平面方程为[tex=25.071x1.357]ZHDnKQos7bcre2k3TRoQmKGYa8aqe4zRZKMxjq6l1xN02NYxCjkOwKGaT/2VkC+YHUpOGckVP2hpI8cwLEIDTgIMWUHt2LcMUxgcgn+tybPeKjufFxlQ0k7dWoIwTmMG0BcV9tDydycaKBBDuvxhQYJPkkDNjV8MGHjq8YrVYKg=[/tex]即[tex=13.071x1.214]Z/ZW+DHcSDX0Hl7uyry46CP3CwUKNwFViP0/PEWtiYL7OB5XLmJzCNbPTw3IqUZ+LN0SJGIhVQ/Ia7JAvi+O4g==[/tex]法线方程为[tex=14.786x2.5]VsEn5aMvNj0a1Q201sXGTru4qMZhoRIQXaQZwgky7zIaM1IU1Q8yEFYcyI49+urZD00aEeTw4Ak1mqxU7bQKScbb5vfStms3W2HgrdacBEmlHGp9LzV7rxqvz+/7zRccFfIbvQhR7FzO3VN8tJOGFg==[/tex]

举一反三

内容

0
求下列函数在指定点[tex=1.357x1.214]nVlWDiaq/AF5IB+/Nxj18A==[/tex]处沿指定方向[tex=0.357x1.0]Le5Jr6QhXJv1Yp4NjrbGVA==[/tex]的方向导数：[tex=6.0x1.143]E8xyJCFOYVTsGJo01Z+Exw==[/tex]，[tex=4.214x1.357]B/uWG509qWollcwzu0jmkA==[/tex]，[tex=0.357x1.0]Le5Jr6QhXJv1Yp4NjrbGVA==[/tex]为沿该点向径方向.
1
证明: 在点[tex=5.571x1.357]5Mv5IhIrcJ0jOelk3DLzinCcGeiQtnSTWnWEClUYx3wrZmO9qiXYsIPL/ySUCbeS[/tex]处,函数 [tex=7.071x1.429]KpCP3f0yVC1ooWVQ1GpC5AgDfjLhpIzDvQfU0AtIPx4=[/tex] 及 [tex=14.357x1.429]5ChPGZLNHqZ2PJedvGqfxAxoJejfwmj8UEo91VMICziSY7n9DkUrSmXOJv/y10oW[/tex]([tex=5.643x1.214]f5gS3rEdYpfc+EroQpRocfRUIBa1BitrODaSh0qwmps=[/tex] 为常数且 [tex=6.0x1.429]2sjA3UQL9lu84Vtwa9TxanERn8skFytJiwaw6DZmmM8=[/tex] )二者的梯度之间的角度当点 [tex=1.357x1.214]nVlWDiaq/AF5IB+/Nxj18A==[/tex] 无限远移时趋于零.
2
已知[tex=5.0x1.286]nNRgYScRPw16N2lBJqtTsA==[/tex]，[tex=5.0x1.286]ZIJz5gTGIgdeWAGMFdoL1A==[/tex]，则[tex=6.214x1.286]wE5wtWoL9HR6uGPZrIzvHA==[/tex]成立的[tex=0.571x1.286]XubEW9+1+hkJqH7jXe5MrA==[/tex]值为 A: 1 B: 2 C: 4 D: 6 E: 8
3
输出九九乘法表。 1*1=1 2*1=2 2*2=4 3*1=3 3*2=6 3*3=9 4*1=4 4*2=8 4*3=12 4*4=16 5*1=5 5*2=10 5*3=15 5*4=20 5*5=25 6*1=6 6*2=12 6*3=18 6*4=24 6*5=30 6*6=36 7*1=7 7*2=14 7*3=21 7*4=28 7*5=35 7*6=42 7*7=49 8*1=8 8*2=16 8*3=24 8*4=32 8*5=40 8*6=48 8*7=56 8*8=64 9*1=9
4
求下列函数的单调区间、凹凸区间、极值点、拐点和渐近线,并绘图(图略).(1) [tex=6.643x1.5]bfylM61K4fB2dxr0OSsfGnNoGCHA31PVTv+V6O1K8rw=[/tex](2)[tex=7.643x1.571]v8BogKFXW30N+HMJ7QR6DhxEDs5D0riUpoj095rhlGc=[/tex](3) [tex=3.714x2.143]X1YpNX45Pb+t3RD9Lv2Xa/npVx6iPUE04M2Y4K2k/cw=[/tex](4) [tex=5.071x3.0]4TWEbfJ+QFPbBo6PXWTsCrjc66tVrHBOTlDUBxhSpARz8/MfCO/nUo/gE3SyIffw[/tex](5)[tex=6.571x2.429]gt+k1kCw/+VFBVaKddmG6PvDvxiTdyZFXDwIPBeuGlw=[/tex](6)[tex=5.643x1.429]Hzyd6Qvm69qjRqgBIuKTx/cTmFyy56Dt2K/GC7NoCdc=[/tex](7) [tex=7.143x1.214]CwtdUElTamN1NqF0aKHeWGdaXEazoOnz3w3c67izzuE=[/tex](8)[tex=4.714x2.786]cxjZEag+Wbr67lAUIC3Slk2OV17yHgezOhFRferr5F0=[/tex].