Publications by Laura Burenkov
Data 605 A14
Taylor Series Expansions of Popular Functions 1. \(f(x) = (1 - x)\) The valid range for this function is \(|x| < 1\). The Taylor Series expansion of \(f(x)\) around \(x = 0\) is: \[ f(x) = \sum_{n=0}^{\infty} \frac{{f^{(n)}(0)}}{{n!}} x^n \] where \(f^{(n)}(0)\) represents the \(n\)-th derivative of \(f(x)\) evaluated at \(x = 0\). For \(f(x) ...
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Discussion 14
Exercises 3 - 6, chapter 8.8 \(f(x) = e^x; \, c = 0\) \ The Taylor series expansion for \(e^x\) around \(c = 0\) is given by: \[ e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} \] Let’s find the first few terms of this series and identify the pattern: \[ f(x) = e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \dots \] The pattern ...
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D621 hwk5
Overview In this homework assignment, you will explore, analyze and model a data set containing information on approximately 12,000 commercially available wines. The variables are mostly related to the chemical properties of the wine being sold. The response variable is the number of sample cases of wine that were purchased by wine distribution...
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Data 605 A13
Problem 1 Use integration by substitution to solve the integral below. 4e^{-7x} , dx Solution: \[\begin{align*} \int 4e^{-7x} \, dx &= \int 4e^{u} \left( \frac{du}{-7} \right) \\ &= \frac{4}{-7} \int e^{u} \, du \\ &= \frac{4}{-7} e^{u} + C \\ &= \frac{4}{-7} e^{-7x} + C \end{align*}\] Problem 2 Biologists are treating a pond contaminated with...
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Discussion 13
Chapter 4 Water flows onto a flat surface at a rate of 5cm3 /s forming a circular puddle 10mm deep. How fast is the radius growing when the radius is: (a) 1 cm? (b) 10 cm? (c) 100 cm? #Relevant data Q <- 5 # Flow rate in cm^3/s h <- 10 # Depth of the puddle in mm, converted to cm dV_dt <- Q # Rate of change of volume, given by the flow rate...
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Story 6
Overview The United Nations Food and Agriculture Organization publication, The State of Food Security and Nutrition in the World 2022 (https://www.fao.org/documents/card/en/c/cc0639en) might lead one to the conclusion that it’s an elsewhere problem. That the people who are suffering malnutrition and starvation are “elsewhere”, not in our ...
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Data 605 A12
Overview The attached who.csv dataset contains real-world data from 2008. The variables included follow. Country: name of the country LifeExp: average life expectancy for the country in years InfantSurvival: proportion of those surviving to one year or more Under5Survival: proportion of those surviving to five years or more TBFree: proportion o...
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Discussion 12
Using R, build a multiple regression model for data that interests you. Include in this model at least one quadratic term, one dichotomous term, and one dichotomous vs. quantitative interaction term. Interpret all coefficients. Conduct residual analysis. Was the linear model appropriate? Why or why not? #Loading data from CSV file data <- rea...
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Data 605 A11
Overview Using the “cars” dataset in R, build a linear model for stopping distance as a function of speed and replicate the analysis of your textbook chapter 3 (visualization, quality evaluation of the model, and residual analysis.) Model #Loading dataset and inspecting its structure data(cars) str(cars) ## 'data.frame': 50 obs. of 2 ...
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Discussion 11
Discussion 11 #Loading package library(readxl) ## Warning: package 'readxl' was built under R version 4.3.3 #Replacing the file path with the correct path to your Excel file file_path <- "C:/Users/aleja/Desktop/Real estate valuation data set.xlsx" #Reading the first 5 rows of the Excel file data <- read_excel(file_path, n_max = 5) #Viewing t...
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