Publications by Dirk Hartog
Discussion board 15
Chapter 12: Exercises 6 and 8 Evaluate \(f_x(x,y)\) and \(f_y(x,y)\) at the indicated point. We need to find the derivatives with respect to x and y separately and then evaluate them at the given point. 6. \(f(x,y) = x^3 - 3x + y^2 -6y ~at ~(-1,3)\) a. Partial derivative with respect to x \(f_x(x,y)\) \(\frac{df}{dx} x^3 - 3x + y^2 -6y\) Differen...
1607 sym
Homework wk14
Assignment 14 - Taylor Series This week, we’ll work out some Taylor Series expansions of popular functions. \(f(x) = (1-x)^{-1}\) \(f(x) = e^x\) \(f(x) = ln(1+x)\) \(f(x) = x^\frac{1}{2}\) For each function, only consider its valid ranges as indicated in the notes when you are computing the Taylor Series expansion. Please submit your assignmen...
3928 sym
Discussion board 14
Chapter 8.8, Exercise 21 & 22 Write out the first five terms of the Binomial series with the given k-values The binomial series expansion for the first five terms for any value of \(k \neq 0\) is as follows: \[ (1+x)^k = 1 + kx + \frac{k(k-1)}{2!}x^2 + \frac{k(k-1)(k-2)}{3!}x^3 + \frac{k(k-1)(k-2)(k-3)}{4!}x^4\] Ex. 21 - When k = \(\frac{1}{2}\) \...
1083 sym
Homework wk13
Question 1: Use integration by substitution to solve the integral below \[\int4e^{-7x}dx\\ ............... \\ u = -7x \\ du = -7dx \\ dx = \frac{du}{-7}\\ \int4e^{u}\frac{du}{-7} \\ -\frac{4}{7}\int e^{u}du = \\ -\frac{4}{7}e^{u} + C \\ -\frac{4}{7}e^{-7x} + C \] Using integration by substitution for \(\int4e^{-7x}dx\) we get \(\frac{4}{7}e^{-7x} +...
4780 sym
Discussion board 13
Chapter 4 Section 4.2: Question 7 page 179 An F-22 aircraft is flyign at 500 mph weieht an elevation of 10,000 feet on a straight-line path that will take it directly over an anti-aircraft gun. How fast must the gun be able to turn to accuratley track the aircraft when the plane is: 1 mile away? 1/5 mile away? Directly overhead? First we want to ...
855 sym
Homework wk12
Introduction 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 ...
4361 sym R (6090 sym/26 pcs) 2 img
Discussion board 12
PROBLEM: Using R, build a multiple regression model for data that interests you. Include in this model: at least one quadratic term one dichotomous term one dichotomous vs. quantitative interaction term Interpret all coefficients. Conduct residual analysis. Was the linear model appropriate? Why or why not? The data set I choose to explore is calle...
3691 sym R (15244 sym/35 pcs) 4 img
Homework wk11
PROBLEM: Using the “cars” dataset in R, build a linear model for stopping distance as a function of speed. Replicate the analysis of your textbook chapter 3 : - Visualization - Quality evaluation of the model - Residual analysis library(tidyverse) ## ── Attaching core tidyverse packages ────────────────�...
2911 sym R (2897 sym/11 pcs) 4 img
Discussion board 11
library(tidyverse) Exercise Week 11 Using R, build a regression model for data that interests you. Conduct residual analysis. Was the linear model appropriate? Why or why not? This data set captures the details of how CO2 emissions by a vehicle can vary with the different features. The data set has been taken from Canada Government official open...
1558 sym R (3687 sym/11 pcs) 2 img
Homework wk10
library(markovchain) ## Package: markovchain ## Version: 0.9.5 ## Date: 2023-09-24 09:20:02 UTC ## BugReport: https://github.com/spedygiorgio/markovchain/issues PROBLEM: Smith is in jail and has 1 dollar; he can get out on bail if he has 8 dollars. A guard agrees to make a series of bets with him. If Smith bets A dollars, he wins A dollars w...
2002 sym R (1972 sym/9 pcs)