2 LIMITS

GROUP WORK 2, SECTION 2.4The Dire Wolf Collects his DueIn this activity we will explore a function that is particularly loved by mathematicians everywhere, sin (π/x).1. Sketch the graph of y = sin (π/x) on the interval [−1, 3].2. It appears that this function is not defined at x = 0, does not have a limit at x = 0, and in fact, does noteven have a right-hand limit.(a) Evaluate sin (π/x) at x = 2 1 , 2 5 ,and 2 9 .(b) Evaluate sin (π/x) for x =4n 2+ 1, n a positive integer, using the pattern from part (a).(c) Evaluate sin (π/x) for x = 1 1 , 1 2 ,and 1 3 . Using this pattern, evaluate sin (π/x) for x = n 1 , n a positiveinteger.(d) Give an argument to show that lim sin (π/x) does not exist.x→0 +63