Homework 15

12. 1. 7

Pick any exercise in Chapter 12 of the calculus textbook. Post the solution or your attempt. Discuss any issues you might have had.

What were the most valuable elements you took away from this course?

rm(list=ls())

Give the domain and range of the multivariable function.

f(x, y)=x2+y2+2 The domain of f(x, y) is all (real) values of x and y. The range of f(x, y) is all values greater than or equal to 2. The smallest that the function can be is when both x and y are 0, meaning that the total value will be 2. And as both x and y are being squared in the function, there is no possibility that f(x, y) can be negative.

f<-function(x,y){x^2 +y^2 + 2}

x<-runif(10000,-1000,1000)
y<-runif(10000,-1000,1000)
result<-f(x,y)

#histogram
hist(result, breaks = 100)

min(result)
## [1] 189.0887

The most valuable elements elements I took from this course were brushing up on math I haven’t practiced in years such as calculus. I learned about some built-in functions in R e.g. pracma