Please answer all the questions with CLEAR FORMAT :) THANKS

EXAMPLE 4 Investigate the following limit. lim sin(Sic) SOLUTION Again the function f(x) = sin(3n/x) is undefined at 0. Evaluating the function for some small values of x, we get F(1) = sin(3n) =[ (= = sin(617) = 0 (4) = sin(97) = (4 ) = sin() =0 F(0.1) = sin(30n) = 0 f(0.01) = sin(300m) = Similarly, f(0.001) = A(0.0001) = 0. On the basis of this information we might be tempted to guess that lim sin (ST ) = but this time our guess is wrong. Note that although f(1) = sin(3nn) = for any integer n, it is also true that f(x) = 1 for infinitely many values of x that approach 0. You can see this from the graph of f given in the figure. The compressed lines near the y-axis indicate that the values of A(x) oscillate between 1 and -1 infinitely often as x approaches 0. (See this exercise.) Since the values of f(x) do not approach a fixed number as x approaches 0, lim sin (Suz ) does not exist. x-0