Math 210, Spring 2013 Lab Quiz #2 Solutions Remember that 2 marks for lab quizzes are given for presentation. Some text discussion of the commands you use is needed to get full marks. Q#1 QyQ+SSJmRzYiLUkkZXhwR0YlNiMtSSRjb3NHRiU2I0kieEdGJSIiIg==

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Convert to a polynomial, then to a function and finally evaluate it at x=1.2 LUkoY29udmVydEclKnByb3RlY3RlZEc2JEkiJUc2IkkocG9seW5vbUdGJA==

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Q#2 Proceed as above to get T3(x) based at x=0. Here, I will leave T3 as an expression. PkkjVDNHNiItSShjb252ZXJ0RyUqcHJvdGVjdGVkRzYkLUkndGF5bG9yR0YnNiVJImZHRiQvSSJ4R0YkIiIhIiIlSShwb2x5bm9tR0Yn

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As a side note, the third derivative at zero is zero, so T3 is the same as T2 when x=0 is the base point. LUklcGxvdEc2IjYnNyRJImZHRiRJI1QzR0YkL0kieEdGJDshIiIiIiIvSSZjb2xvckdGJDckSSZibGFja0dGJEklYmx1ZUdGJC9JKnRoaWNrbmVzc0dGJDckIiIkIiIhL0kqbGluZXN0eWxlR0YkNyRJJnNvbGlkR0YkSSVkYXNoR0Yk

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From the form of f we could deduce the limit, but this is confirmed by the Maple command below. LUkmbGltaXRHNiI2JEkiZkdGJC9JInhHRiRJKWluZmluaXR5RyUqcHJvdGVjdGVkRw==

IiIj

You could investigate the Maple command, maximize, but I decided to find the root of the derivative where it is clear the maximum occurs QyQ+SSNkZkc2Ii1JJWRpZmZHJSpwcm90ZWN0ZWRHNiRJImZHRiVJInhHRiUiIiI=

LCgqKCwmSSJ4RzYiIiIlIiM1IiIiRiksJkYlRilGKUYpISIiLCZGJUYpIiIjRilGK0YpKigsKCokRiVGLUYtRiVGKEYrRilGKUYqISIjRixGK0YrKihGL0YpRipGK0YsRjFGKw==

LUknZnNvbHZlRzYiNiQvSSNkZkdGJCIiIS9JInhHRiQ7IiIiIiIl

JCIrZE07YVIhIio=

This is the x value where the maximum occurs, we can then evaluate f there to get the maximum value LUklZXZhbEclKnByb3RlY3RlZEc2JEkiZkc2Ii9JInhHRidJIiVHRic=

JCIrW0JwbUIhIio=

From the graph that looks about right. Q#4 Proceed as above to get T3 QyQ+SSJmRzYiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMqJkkieEdGJSIiIi1JJHNpbkdGKDYjRi1GLkYu

LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJkkieEdGJyIiIi1JJHNpbkdGJDYjRipGKw==

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LCYiIiJGIyokSSJ4RzYiIiIjRiM=

Do some plotting to see where the roots of f-T3 are LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLCZJImZHRiciIiJJI1QzR0YnISIiL0kieEdGJzshIigiIig=

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The roots are 0 and +/- x1, x2 where x1 and x2 are given below PkkjeDFHNiItSSdmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JCwmSSJmR0YkIiIiSSNUM0dGJCEiIi9JInhHRiQ7Ri0iIiQ=

JCIrM2Y3NkEhIio=

PkkjeDJHNiItSSdmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JCwmSSJmR0YkIiIiSSNUM0dGJCEiIi9JInhHRiQ7IiInIiIo

JCIrRyRIPilvISIq