Define the function F: [0, 1] → R by: = F(1) - dz √ 1+x2 xt dx Tasks: 1. Function Analysis: • • a. Determine whether F(t) is differentiable on [0, 1]. b. If differentiable, compute F'(t) using differentiation under the integral sign. 2. Graphical Representation: ⚫ a. Plot F(t) fort € [0,1]. ⚫ b. Plot F' (t) alongside F(t) to illustrate the relationship between the function and its derivative. 3. Histogram of Integrand Values: ⚫ a. For a fixed t, construct a histogram of the values • as a varies over [0, 1]. b. Analyze how the histogram changes as t increases from 0 to 1. 4. Numerical Approximation: ⚫ a. Use numerical integration methods to approximate F(t) and F'(t) for various t. • b. Compare the numerical results with the analytical expressions obtained.

I have to create a frequency table using model of trucks for class and the YDT sales as the frequencies, would I write down the YTD numbers from he sales as the frequencies or how do I find the frequencies ?

• Open RStudio. • Open a new R Script. • Copy and paste the below code in R. (to present your answer for this task, take a screenshot of your RStudio session, and paste it into your assessment solutions document). • Run the code, then copy and paste the outputs and the graphs into your assessment solutions document. • Copy and paste the code in your assignment and use comments to explain each line of the code. Note: to get help in R, highlight the code and press F1. Code to be copied and pasted into an R script in RStudio: Treatment <- rep (c("Level_1", "Level_2","Level_3"), each=10) Response <- c(11, 8, 10, 12, 8, 12, 9, 9, 4, 12, 12, 9, 12, 10, 18, 24, 17, 16, 20, 11, 14, 7, 18, 8, 12, 10, 9, 14, 12, 10) Data Question_3<-data.frame(Treatment, Response) View(Data_Question 3) aggregate (Data Question_3$Response, list (Data Question_3$Treatment), mean) aggregate (Data_Question_3$Response, list (Data Question_3$Treatment), sd) aggregate (Response Treatment, Data Question 3, function…

The whole data set will be in the two pictures