3d gradient, level surface tangent plane and normal lineTemplate for homework (delete this title in copy to your worksheet, edit the comments so they become yours!)Template for plotting level surface, tangent plane and normal line once calculated by hand and input on the right hand sides of the following inputs:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC8lK2V4ZWN1dGFibGVHRj1GOQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJnBsb3RzRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAtSSNtb0dGJDYtUSI6RidGQC8lJmZlbmNlR0Y/LyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlZGPUZAHere is a Maple function and its gradient at a particular point: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 create the 3 plots, choose 1-1 scaling or not depending on circumstances (yes for ellipsoid example). By trial and error we get just the whole isotherm without wasting additional valuable space in our boxed axes windowLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEvaW1wbGljaXRwbG90M2RGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUTAmQXBwbHlGdW5jdGlvbjtGJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUy1JKG1mZW5jZWRHRiQ2JC1GIzZJLUYsNiVRImZGJ0Y2RjktRlc2JC1GIzYpLUYsNiVRInhGJ0Y2RjktRj02LVEiLEYnRkBGQi9GRkY4RkdGSUZLRk1GT0ZRL0ZVUSwwLjMzMzMzMzNlbUYnLUYsNiVRInlGJ0Y2RjlGX28tRiw2JVEiekYnRjZGOS8lK2V4ZWN1dGFibGVHRkRGQEZALUY9Ni1RIj1GJ0ZARkJGRUZHRklGS0ZNRk8vRlJRLDAuMjc3Nzc3OGVtRicvRlVGYXAtSSNtbkdGJDYkUSI1RidGQEZfb0Zcb0ZdcC1GPTYtUSomdW1pbnVzMDtGJ0ZARkJGRUZHRklGS0ZNRk8vRlJRLDAuMjIyMjIyMmVtRicvRlVGW3EtRmRwNiRRJDIuNUYnRkAtRj02LVEjLi5GJ0ZARkJGRUZHRklGS0ZNRk9GanBGVEZdcUZfb0Zlb0ZdcEZncC1GZHA2JFElMS43NUYnRkBGYHFGY3FGX29GaG9GXXBGZ3BGY3FGYHFGY3FGX28tRiw2JVElYXhlc0YnRjZGOUZdcC1GLDYlUSZib3hlZEYnRjZGOUZfby1GLDYlUShzY2FsaW5nRidGNkY5Rl1wLUYsNiVRLGNvbnN0cmFpbmVkRidGNkY5Rl9vLUYsNiVRJnN0eWxlRidGNkY5Rl1wLUYsNiVRKHN1cmZhY2VGJ0Y2RjlGW3BGQEZARltwRkBGK0ZbcEZALUY9Ni1RIjtGJ0ZARkJGYm9GR0ZJRktGTUZPRlFGYnBGW3BGQA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEjcDFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSIlRidGL0YyLUY2Ni1RIjpGJ0Y5RjtGPkZARkJGREZGRkhGSkZNLyUrZXhlY3V0YWJsZUdGPUY5By trial and error we (you too!) choose the window to be on the same scale as the surface for both the plane and normal line: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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEjcDNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSIlRidGL0YyLUY2Ni1RIjpGJ0Y5RjtGPkZARkJGREZGRkhGSkZNLyUrZXhlY3V0YWJsZUdGPUY5Then display and click on the plot and rotate to check that the tangent plane is tangent and the normal line is perpendicular and passes through the point of tangency:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUShkaXNwbGF5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2LS1GLDYlUSNwMUYnRjRGNy1GOzYtUSIsRidGPkZAL0ZERjZGRUZHRklGS0ZNRk8vRlNRLDAuMzMzMzMzM2VtRictRiw2JVEjcDJGJ0Y0RjdGZm4tRiw2JVEjcDNGJ0Y0RjdGZm4tRiw2JVEoc2NhbGluZ0YnRjRGNy1GOzYtUSI9RidGPkZARkNGRUZHRklGS0ZNL0ZQUSwwLjI3Nzc3NzhlbUYnL0ZTRmlvLUYsNiVRLGNvbnN0cmFpbmVkRidGNEY3LyUrZXhlY3V0YWJsZUdGQkY+Rj5GXnBGPkYrRl5wRj4=Make some comment here about whether it looks right. If your tangent plane equation or normal line are wrong, it will be obvious.