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solve them pl
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i to u
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4. (6 Points). Use the method of cylindrical shells to find the volume generated by
rotating about the linex=-1 the region bounded by the curves
y=4-2x, y=0, x=0
2
Sotto de
d
2
1.1.2.2014
ال
ho llen
on the interval 0, 2)
5. (6 Points). Consider the function $(x) = 2xe
a) Find the average value, faw, of Rx)
fan una
Pawn [ 23 Sene") de
od Sach
b) Find numbers, c, such that fove = f(c).
suppose
are -
then 1910)-2
= 2
ce - 1.
5
Bonus Problem:
6. (6 Points). Multiple Choices: NO PARTIAL CREDIT
Circle the letter of the correct answer. (2 Points each).
i. The Area of the shaded region below is given by
c. 12y-y?)-(y2 - 4y)]dy
D. LI(2y-y)-y-4y)] de
@L'to-4»)-(28-y?)dy
B. 102-4y)-(2y - y?)]dx
X Х
x=y? - 4y
3.3)
) لا
x=2y-y2
ii. The region bounded by the line y = 2-x and the two axes is revolved about
the .r-axis. The volume of solid generated, using Cross sections, is
2. (6 Points). Find the area of the region enclosed by the curves
1
y= Vad y = -x, x=9
2
=vxl
17
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Boston University Time Series in R Composition
This assignment provides practice in decomposing the seasonal time series data and then subtract that effect from the data ...
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This assignment provides practice in decomposing the seasonal time series data and then subtract that effect from the data and then to show how to address issues of correlations between successive values of the time series. Before beginning this assignment, review the learning resources for this module, especially focus on Decomposing Time Series, Forecasting using Exponential Smoothing and ARIMA Models sections of A Little of R for Time Series by Avril Coghlan. Complete the following steps and write a report to record your work, results and analysis. You may use the attached data sets (average price data and NY benchmarked employment data) or one of time series data from data( ). Please note that some time series are more amenable to time series analysis than others.It is important that you understand data structure and be able to appropriately transform/clean raw data prior to analysis. "Average price data.xlsx" is in the long format. The data series are stacked on top of each other. That is how the data is provided the Bureau of Labor Statistics. The names of variables are provided in the "series" worksheet. You need to pick one series name and use it to filter or subset the data prior to analysis. Some series are better than others. You may want to use only the portions of the series after 2009, since the Great Recession was an one-time event that cannot be modeled.A. Decompose seasonal time series data and subtract that effect from the data:
Identify an appropriate time series data set, this can be a data set in R or a data set you find.
Then, use R to display decompose the seasonal time series and seasonally adjust to subtract the seasonal components from the time series.
In your report, provide insights to the results.
B. Address issues of correlations between successive values of the time series:
Identify an appropriate data set, this can be this can be a data set in R or a data set you find.
Then use R time series functions to address autocorrelation issues in data sets. In many cases you can make a better predictive model by taking correlations in the data into account. Address autocorrelation issues (irregular components of the time series) using a technique called ARIMA (Autoregressive Integrated Moving Average) models for irregular components of time series.
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