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Sequencs Be sure Probletn Find closed formulas for the terms for the following two indicate the starting value 0f the indee:-4310,17.24,31_03 8.15,24,35, 18_...

Question

Sequencs Be sure Probletn Find closed formulas for the terms for the following two indicate the starting value 0f the indee:-4310,17.24,31_03 8.15,24,35, 18_

sequencs Be sure Probletn Find closed formulas for the terms for the following two indicate the starting value 0f the indee: -4310,17.24,31_ 03 8.15,24,35, 18_



Answers

Use a calculator to find the approximate value of each expression. Round the answer to two decimal places. $\cot \frac{\pi}{18}$

All right. We want to calculate the value given by sign of 0.3 65.3 65 is in radiance. Using a series expansion including and equals three terms. This question is shallow. Your ability to apply series in particular to challenge your ability to apply the MacLaurin series for the purpose of evaluating the function at a point remember the section we learned five point MacLaurin series. They are a three here. E X. Sign X. Cosign X one plus X and one plus. Actually end for this problem. We clearly need to use the sine function be for three terms we have to use the three terms. That's it on the screen extra. Actually over five factorial. Thus we can plug in 50.3 65 wherever we see X. And something our three terms to obtain the approximation. So using B we have 30.3 65 minus 650.3 65 cube over three factorial plus 30.3 65 55 factorial summing these constants. We have value 550.35461 for signs 0.3 65 the calculated value is the same 650.35461

We want to calculate the value below with a series expansion at n equals three for eat to the point to power the race. The power point to this question is challenging our ability to apply MacLaurin series expansions of typical functions for calculating functions at a particular point. So we need to have an understanding of the general MacLaurin series for functions such as this one. So there are five key MacLaurin series. We need to know these are for easy X. Sign X. Cosign X. Ln one plus X and 1% at the end. And this particular problem we option A. That is the series expansion for E to the X. Where in this case we're gonna plug in X equals 10.2. So using the series expansion we have E the 0.2 equals one plus 10.2 plus 0.2 squared over two. For an equal three terms, we use one plus X. Was expert over two factorial. Thus we have one plus 10.2 plus 0.2 Thus our series approximation is 1.22 on a calculator. We would get something more specific. 1.2 to 14

We want to calculate the value given by sine of 0.1 where 1.1 ingredients with a series expansion for and equals two. In order to calculate this, we need to have an understanding of the application of MacLaurin series, particularly how we can use MacLaurin series expansion to calculate the value of this function at a point. So remember the Colin MacLaurin series that we use solve problems to this one. Are a three here which are for the oxen, exco sex Ellen one plus X and one plus actually and respectively. Clearly in this particular problem we need to use the sign X function be for two terms we're gonna use x minus executed over three factorial. Where to make this approximation, we plug in 30.1 for X. So using the we have signed a 0.1 equals 0.1 minus 0.1 Q over three factorial or 30.1 minus 0.1 divided by six. This has value 60.99983 Which we compare to the calculator value of 0.99833

We want to calculate the value. Using a series expansion, including n equals three times the value we want to calculate is 1.1 raised to the exponential power of negative zero point to this question is challenging our understanding of how to apply series expansion towards the purpose of evaluating the function at a point. So remember the five MacLaurin series expansion that we've learned in this section are a three here which are one E X, Synnex co sex and one plus X and one plus. Actually, um respectively. As a very in order to below, we're going to be using E which is one plus actually and where in this case excess 10.1 and is negative two brand equals three terms. We need to use all three terms. Listen here one plus mx plus and emptiness and 1/2 factorial X squared plus. We have one plus negative 10.2 times 0.1 plus negative 0.2 times negative one point 2/2 times 1.0.1 square as our approximation. If we some of these terms we obtain solution for this problem, 0.9812 This is very close to the calculated value of 0.9811


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