This example shows that using a Maclaunn polynomial of degree 5 gives us the value of e, accurate to 2 decimal places. (This is a hint that you may want to read this example before proceeding.) Now, some questions. To answer, please refer to the GeoGebra applet provided (click the link to access the applet, or paste https:llmvw.geogebraorglmlkdeTjhf into your browser}. (a) (2 points} Using the slider labelled 1;, determine what degree is necessary to get the value of e, accurate to 5 decimal places. (Is it more or less than you expected?) Note: if x) 2 3*, then 8 = 31 = l) can be approximated using 10(1), where p is a Maclaurin polynomial for 3'. You should only be adjusting the value of n in the applet. The values for zz) and a are set correctly. The value u.) p(a) that is calculated for you tells you how much the error is. (b) (2 points} If you instead wanted to approximate the value of 82 using the same polynomial from part (a), how accurate would your answer be? (You will want to change a = 1 to a = 2.} (c) (2 points)All of the above relies on prior knowledge of the value of 8. Imagine that the only thing we knew about 3 was that its value was somewhere between 2 and 3. Explain how we could use Taylor's Theorem to know that our answer in part (a) is accurate, despite not knowing the value of 3. Hints for part {c}: Taylor's Theorem states that for a given function x] (that meets certain "niceness" conditions}, the degree 71 Taylor polynomial satises flit) = 1:41?) + RAE), where the remainder, RAE] gives a measure of the error in approximating x} by p43}. We typically ask what the biggest possible value for Raw) could be, to get an idea of the maximum {worst case scenario} error. If we can make the maximum error small, we know that the true error will be even smaller. In the case of a Maclaurin polynomial for the exponential function, we get I] where 2: is some number between 0 and I. (So lfI : 1, a\" will be somewhere between a = 1 and 31 = e, which we are assuming is no bigger than 3.}