Publications by Tora Mullings
605 - Final
library(knitr) # for table of counts library(kableExtra) library(tidyverse) # for %>% operator library(moments) # skewness and kurtosis library(hrbrthemes) # themes library(DescTools) # mode library(scales) # remove sci notation library(corrplot) library(factoextra) # pca scree plot library(MASS) # fitdistr train.df <- read.csv("t...
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605 - HW 15
Q1 x <- c(5.6, 6.3, 7, 7.7, 8.4) y <- c(8.8, 12.4, 14.8, 18.2, 20.8) model <- lm(y ~ x) summary(model) ## ## Call: ## lm(formula = y ~ x) ## ## Residuals: ## 1 2 3 4 5 ## -0.24 0.38 -0.20 0.22 -0.16 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) -14.8000 1.036...
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605 - Discussion Week 15
Chapter 12.8, Q7 Find the critical points of the given function. Use the Second Derivative Test to determine if each critical point corresponds to a relative maximum, minimum, or saddle point. \(f(x,y) = x^2 + 3y^2 - 6y + 4xy\) Below is AI-generated code that produces a plot of the function. # Define the function f(x, y) f <- function(x, y) { ...
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605 - Discussion Week 14
Chapter 8.8, # 27 Find the Taylor Series for \(f(x)=sin(2x+3)\). From Key Idea 8.8.1, and Theorem 8.8.2, if we let \(f(x) = sin(x)\) and \(h(x) = 2x+3\), then \(sin(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!} \cdot x^{2n+1}\) Therefore, \[\begin{align*} f(h(x)) & = sin(2x+3) \\ & = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!} \cdot (2x+3)^n \...
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605 - HW 14
Taylor Series Expansions The Taylor polynomial of degree \(n\) of \(f\) at \(x=c\) is: \(p_n(x) = f(c) + f'(c)(x-c) + \frac{f''(c)(x-c)^2}{2!} + \frac{f'''(c)(x-c)^3}{3!} + ...+ \frac{f^{(n)}(c)(x-c)^n}{n!}\) \(f(x) = \frac{1}{1-x}\) Step 1: Find the first \(n\) derivatives of \(f(x)\). \(f(x) = \frac{1}{1-x}\) \(f'(x) = \frac{1}{(1-x)^2}\) ...
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605 - HW 13
Q1 Integrate by substitution: \(\int{4e^{-7x} \ dx}\) Let \(u\) = \(e^{-7x}\) \(\frac{du}{dx} = -7e^{-7x}\) \(du = -7e^{-7x} \ dx\) \(\frac{-du}{7} = e^{-7x} \ dx\) Substitute: \(\int{4 \cdot \frac{-du}{7}}\) \(\frac{-4}{7} \int{du}\) \(\frac{-4}{7} \cdot u\) \(\frac{-4}{7} \cdot e^{-7x}\) Q2 \(\frac{dN}{dt} = \frac{-3150}{t^{4}} - 220\) Integra...
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605 - Discussion Week 13
Question 4.14 A hot air balloon lifts off from the ground rising vertically. From 100 feet away, a 5’ woman tracks the path of the balloon. When her sightline with the balloon makes a \(45^\circ\) angle with the horizontal, she notes the angle is increasing at about \(5^\circ\) per minute. (a) What is the elevation of the balloon? (b) How fast...
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HW 12 - 605
df <- read.csv("who.csv", header=TRUE) head(df) ## Country LifeExp InfantSurvival Under5Survival TBFree PropMD ## 1 Afghanistan 42 0.835 0.743 0.99769 0.000228841 ## 2 Albania 71 0.985 0.983 0.99974 0.001143127 ## 3 Algeria 71 0.967 ...
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Discussion week 12 - 605
library(tidyverse) df <- datasets::quakes df_dich <- df %>% mutate(station_bin = cut(stations, breaks=c(0, 10, 20, 30, 40, 50))) head(df_dich) ## lat long depth mag stations station_bin ## 1 -20.42 181.62 562 4.8 41 (40,50] ## 2 -20.62 181.03 650 4.2 15 (10,20] ## 3 -26.00 184.10 42 5.4 43 (40,50] #...
103 sym R (1818 sym/5 pcs)
HW 11 - 605
Cars Dataset library(tidyverse) df <- datasets::cars summary(df) ## speed dist ## Min. : 4.0 Min. : 2.00 ## 1st Qu.:12.0 1st Qu.: 26.00 ## Median :15.0 Median : 36.00 ## Mean :15.4 Mean : 42.98 ## 3rd Qu.:19.0 3rd Qu.: 56.00 ## Max. :25.0 Max. :120.00 Visualize plot(cars$speed, c...
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