MAT2500-01 13S Quiz 6 Print Name (Last, First) _________________________________|__Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use arrows and equal signs when appropriate. Always SIMPLIFY expressions. BOX final short answers. LABEL parts of each problem. Keep answers EXACT (but give decimal approximations for interpretation when appropriate). Indicate where technology is used and what type (Maple, GC).1. 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a) Write an equation for the level surface of this function passing through LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=b) Evaluate the gradient vector field and its value at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, identifying it with its proper symbol.
c) In what direction (unit vector) at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= does LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= increase the most rapidly and what is its rate of change in that direction?d) Write an equation for the normal line to the level surface through LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= , namely the line through this point which is aligned with the gradient vector there. At what point 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 does the normal line intersect the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= plane?e) Write an equation for the tangent plane at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and simplify it to integer coefficients.
f) What is the directional derivative of f at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= in the same direction as the vector LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYmLUYjNigtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JFEiMkYnRjRGN0ZRRjRGNC8lJW9wZW5HUScmbGFuZztGJy8lJmNsb3NlR1EnJnJhbmc7RidGNA==? Identify it by its proper symbol. Is the function increasing or decreasing in this direction?solutionQygtSSV3aXRoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMmSShTdHVkZW50R0YnNiNJL1ZlY3RvckNhbGN1bHVzR0YlISIiLUksQmFzaXNGb3JtYXRHRig2I0kmZmFsc2VHRiZGLi1GJDYjSSZwbG90c0dGJUYuQyc+SSJmRzYiZio2JUkieEdGJUkieUdGJUkiekdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiY5JCIiJC1JJXNxcnRHRiU2IywmKiQ5JSIiIyIiIiokOSZGN0Y4RjhGJUYlRiVGOC1GJEYnRjgtRiQ2JUY4RjAiIiU=b)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZALUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInhGJ0YyRjUvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RIj1GJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGWS1GLzYlUSJERicvRjNGP0ZALUkobWZlbmNlZEdGJDYmLUYjNiUtSSNtbkdGJDYkUSIxRidGQEY9RkBGQC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJy1GW282JC1GIzYlRi5GPUZARkAtRltvNiQtRiM2KUY6LUZGNi1RIixGJ0ZARkkvRkxGNEZNRk9GUUZTRlUvRlhRJjAuMGVtRicvRmVuUSwwLjMzMzMzMzNlbUYnLUYvNiVRInlGJ0YyRjVGYXAtRi82JVEiekYnRjJGNUY9RkBGQC1GRjYtUSI7RidGQEZJRmRwRk1GT0ZRRlNGVUZlcEZaLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRmZwLyUmZGVwdGhHRmdxLyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUYsNiVGLi1GIzYlRmlwRj1GQEZCRkVGZm4tRltvNiYtRiM2JS1GYG82JFEiMkYnRkBGPUZARkBGY29GZm9GaW9GXXBGX3FGYnEtRmNxNiZGZXFGaHFGanEvRl1yUSVhdXRvRictRiw2JUYuLUYjNiRGXHFGQEZCLUYvNiNRIUYnRmpyRkVGZm4tRltvNiYtRiM2JC1GYG82JFEiM0YnRkBGQEZARmNvRmZvLUZbbzYkLUYjNiRGLkZARkAtRltvNiQtRiM2KEY6RmFwRmlwRmFwRlxxRkBGQEZic0ZicUZic0Y9RkA=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEnZ3JhZGYwRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEpc2ltcGxpZnlGJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2JS1GUzYnLUYjNjAtRiw2JVEiREYnL0YwRj1GOS1GUzYmLUYjNiQtSSNtbkdGJDYkUSIxRidGOUY5RjkvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRictRlM2JC1GIzYkLUYsNiVRImZGJ0YvRjJGOUY5LUZTNiQtRiM2KEZdby1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUZebzYkUSIzRidGOUZicC1GXm82JFEiNEYnRjlGOUY5LUY2Ni5GZHAvJStleGVjdXRhYmxlR0Y9RjlGO0ZlcEZARkJGREZGRkhGZnBGaHBGZW4tRlM2Ji1GIzYkLUZebzYkUSIyRidGOUY5RjlGYW9GZG9GZ29GXnBGYnAtRiM2J0Zlbi1GUzYmLUYjNiRGanBGOUY5RmFvRmRvRmdvRl5wRjktRiw2I1EhRidGYnFGOUZicUY5L0Zib1EnJmxhbmc7RicvRmVvUScmcmFuZztGJ0ZicUY5RjlGYnFGOQ==e)The difference vector and its direction areLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkobWZlbmNlZEdGJDYmLUYjNiktSSNtbkdGJDYkUSIxRidGOS1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUZVNiRRIjJGJ0Y5RlhGam4vJStleGVjdXRhYmxlR0Y9RjlGOS8lJW9wZW5HUScmbGFuZztGJy8lJmNsb3NlR1EnJnJhbmc7RidGXW9GOQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEldWhhdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkmbWZyYWNHRiQ2KC1GIzYlLUYsNiVRInVGJ0YvRjJGL0YyLUYjNictRiw2I1EhRictRiM2JUZZLUkmbXNxcnRHRiQ2Iy1GIzYmRlQtRjY2LVEpJm1pZGRvdDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMTY2NjY2N2VtRicvRk5GYW9GVEY5RjlGWUYvRjIvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmhvLyUpYmV2ZWxsZWRHRj0vJStleGVjdXRhYmxlR0Y9Rjk=The directional derivative is the dot product of the gradient with the unit vector direction: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) the direction vector of the gradient itself gives the direction of maximum increase of the function, while its magnitude gives the rate of change in that direction: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c) d)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Intersection with plane 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desired point is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiktSSNtb0dGJDYtUSomdW1pbnVzMDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGOS8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y5LyUnYWNjZW50R0Y5LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGSC1JI21uR0YkNiRRIzc0RidGNC1GMTYtUSIsRidGNEY3L0Y7USV0cnVlRidGPEY+RkBGQkZEL0ZHUSYwLjBlbUYnL0ZKUSwwLjMzMzMzMzNlbUYnLUZMNiRRIjBGJ0Y0Rk9GWEY0RjRGNA==.why no pretty graphic on the quiz this timeTo tell the truth, it is too flat so the tangent plane does not distinguish itself very well from the function surface itself.With technology we might as well add in the level surface through the point P.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in on the tangent plane and surface.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This is an ugly implicit plot. We can solve for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= as a function of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtaUdGJDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJ6RidGNEY3Rj5GPkY+:
QyUvLUkiZkc2IjYlSSJ4R0YmSSJ5R0YmSSJ6R0YmLUYlNiUiIiIiIiQiIiVGLS1JJnNvbHZlR0YmNiRJIiVHRiZGKA==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QyYtSSdwbG90M2RHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2KC1JJDwsPkdGJzYlLUkiK0dGJjYkLUYuNiQtSSIqR0YmNiQiIiUjIiIiIiIkLUkiLUc2JEYmL0krbW9kdWxlbmFtZUdGKEkvVmVjdG9yQ2FsY3VsdXNHNiVGJkYmL0Y9SShTdHVkZW50R0YnNiMtRjM2JCNGNyIjREkieUdGKC1GOjYjLUYzNiQtRjM2JEY1I0Y3IiN2SSJ6R0YoRkdGUC9GRzsiIiEiIicvRlA7RlMiIikvSSVheGVzR0YoSSZib3hlZEdGKC9JJnN0eWxlR0YoSShzdXJmYWNlR0YoL0kmY29sb3JHRihJJWdyYXlHRihGNz5JLHBsb3R0YW5nb29kR0YoSSIlR0YoISIiLUkoZGlzcGxheUc2IjYkSSlwbG90Z29vZEdGJEkscGxvdHRhbmdvb2RHRiQ=This 1/6 power function in the denominator is exaggerating the behavior of the function, making it rise quickly near the origin inside the unit circle in the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= plane, but also flattening it out outside the unit circle in the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= plane.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=