MAT2500-01 13S Quiz 5 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 problem. Keep answers EXACT (but give decimal approximations for interpretation when appropriate). Indicate where technology is used and what type (Maple, GC).1. a) Use implicit differentiation to evaluate 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 and 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 at the point 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 of the sphere 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 .
b) Write an equation for the tangent plane to this sphere at this point using this information and simplify it to the standard form 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=.
2. Evaluate the linear approximation LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEpJiM1ODUzOTtGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Ji1GLDYlUSJMRidGL0YyLUkjbW9HRiQ2LVEiLEYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJLRidGL0YyRkFGQUZB to the Cobb-Douglas production function 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 at the point LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtbkdGJDYkUSMxNkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0Y0LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnRjBGNEY0RjQ= and use it to approximate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUkjbW5HRiQ2JFEjMTdGJy9GM1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GOzYkUSMxNUYnRj5GPkY+Rj4= .
3. The surface area of a torus (donut!) of cross-section radius LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and circumferential radius LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is 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. For a torus with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjJGJ0Y5Rjk= and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjNGJ0Y5Rjk=, use the differential approximation to estimate the percentage increase in surface area if both dimensions increase by 1 percent.solution1.
Using right click choices to differentiate, solve for. then substitute in (no right click for this)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.a) This is easier to do by hand, since there is no need to multiply through the 1.01 factor until the very end.QyU+SSJQRzYiZio2JEkiTEdGJUkiS0dGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCQqJjkkIyIiJCIiJTklIyIiIkYyIyIkLCIiJCsiRiVGJUYlISIiLUYkRic=QyUtLSZJIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyIiIjYjSSJQR0YqNiRJIkxHRipJIktHRipGLC0tJkYmNiMiIiNGLUYvQyctSSJQRzYiNiQiIztGJyIiIi0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjRig2I0YkRiZGKC0tJkYsNiMiIiNGMUYmQyU+SScmUHNjcjtHNiJmKjYkSSJMR0YlSSJLR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsKC1JIlBHRiU2JCIjO0YxIiIiKiYtLSZJIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2I0YyNiNGL0YwRjIsJjkkRjIhIztGMkYyRjIqJi0tJkY3NiMiIiNGPEYwRjIsJjklRjJGP0YyRjJGMkYlRiVGJUYyLUYkRic=QyctSScmUHNjcjtHNiI2JCIjPCIjOiIiIi1JJmV2YWxmRyUqcHJvdGVjdGVkRzYjSSIlR0YlRiktRis2Iy1JIlBHRiVGJg==3.Qyc+SSJTRzYiZio2JEkickdGJUkiUkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCQqKEkjUGlHJSpwcm90ZWN0ZWRHIiIjOSRGMTklIiIiRjFGJUYlRiVGNC0tJkkiREc2JEYwSShfc3lzbGliR0YlNiNGNDYjRiRGJ0Y0LS0mRjg2I0YxRjxGJw==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If 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, then 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. Thus 3 percent. Done.JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=