![1. Consider the function y f(x) defined by Supposing that you are given x, write an R expression for y using if state- ments Add your expression for y to the following program, then run it to plot the function f. # input x,values <-seq(-2, 2, by 0.1) # for each x calculate y n <- length(x.values) y.values <- rep(0, n) for (i in 1 :n) x <- x. values[i] # your expression for y goes here y.values ij <- y # output plot(x.values, y.values, type1) Your plot should look like Figure 3.2. Do you think f has a derivative at 1? What about at 0? We remark that it is possible to vectorise the program above, using the ifelse function.](http://img.homeworklib.com/questions/49ee0f00-73c8-11ea-8bc4-61639b005272.png?x-oss-process=image/resize,w_560)
Homework Answers
R-code:
![Console Terminal x. values-seq-2,2,by-0.1) > n-length(X. values) > y. values rep (0,n) > y=0 > for (i in 1:n) x=x. values [i] +if (x<-0) +else if { y.values [i]-y (x<-1) y=XA2 else y=sqrt (x) > piot (x.values.y.values,type=1 , mai n=function of x)](http://img.homeworklib.com/questions/4a6d2bc0-73c8-11ea-8865-9da636dcc8fc.png?x-oss-process=image/resize,w_560)
Output:
i) No, f is not derived at x = 1 since f(x) is not continuous at x = 1
ii) Yes, f is derived at x = 0 since f(x) is continuous at x = 0
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