Question 1

Arrange the following decimals from greatest to least.

\[\text{Decimals} = [59.268,521.306,563.08,536.987]\]

# install.packages("tidyverse")
library(tidyverse)
## Warning: package 'lubridate' was built under R version 4.5.2
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.4     ✔ readr     2.1.5
## ✔ forcats   1.0.1     ✔ stringr   1.5.2
## ✔ ggplot2   4.0.0     ✔ tibble    3.3.0
## ✔ lubridate 1.9.4     ✔ tidyr     1.3.1
## ✔ purrr     1.1.0     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
q1_data <- data.frame(Decimals = c(59.268,521.306,563.08,536.987))
q1_data %>%
  arrange(desc(Decimals))
##   Decimals
## 1  563.080
## 2  536.987
## 3  521.306
## 4   59.268

Question 2

Graph the corresponding polygon given the data below.

# install.packages("tidyverse")
library(tidyverse)
q2_data <- data.frame(x = c(5,0,-3,-4,1,4,6,8,8),
                      y = c(8,4,5,-4,-3,1,0,3,6))
ggplot(q2_data,aes(x = x,y = y)) +
  geom_polygon(fill = "steelblue",col = "black",lwd = 1.25) +
  geom_point(size = 4) +
  coord_equal() +
  theme_gray()

Question 3

Differentiate \(f(x) = x^2 \sin^{-1}(x)\).

# install.packages("Deriv")
library(Deriv)
f <- function(x) {
  x^2 * asin(x)
}
f_prime <- Deriv(f)
f_prime
## function (x) 
## x * (2 * asin(x) + x/sqrt(1 - x^2))