MAT2705-02/06 09F Quiz 7 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). Indicate where technology is used and what type (Maple, GC).
1. 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 .a) Verify that the general solution 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 actually solves the DE.b) Using 2x2 matrix methods find the solution which satisfies the initial conditions, showing all work.c) Use technology to plot your result for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5LUY2Ni1RIy4uRidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZOUSYwLjBlbUYnLUZQNiRRIjVGJ0Y5Rjk= and make a rough sketch of what you see, labeling the axes with variable names and key tickmarks on your sketch.d) Use calculus to determine exactly by hand (rules of exponents and logs!) the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= values of the obvious maximum point on the graph and then their approximate values to 4 significant digits, but if you get stuck on solving the derivative condition exactly, use technology to find the approximate values to 4 decimal places in any way you can. Do the numbers you found agree with what your eyes see in the technology plot? [Yes or no, with an explanation would be a good response.]solution1. 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a)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b)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The maximum is at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtbkdGJDYkUScwLjYxMDlGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGNC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYkUSc0LjQyMDhGJ0Y0RjRGNC1GODYtUSIuRidGNEY7L0Y/Rj1GQUZDRkVGR0ZJRksvRk9GTUY0 Clicking on the peak of the graph below gives about (.6,4.4) which agrees with this hand calculation: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 initial conditions in matrix form are: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 solution: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JSFHThese numbers agree with our approximate values above.TTdSMApJNlJUQUJMRV9TQVZFLzE1MDg5MTQwMFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIywmJSNDMUciIiIlI0MyR0YpLCZGKCEiI0YqIyEiIiIiIzYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjIwMTQ0MFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIyIiJCIiJzYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjIwMDU0OFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIyUiIyIjIyEiIiIiJCMiIiVGKSMhIiNGKSMiIiNGKTYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjIxOTkwOFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIyUjQzFHJSNDMkc2Ig==TTdSMApJNlJUQUJMRV9TQVZFLzE1MjIzODQ0MFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIyEiJiIiKTYi