Calculating limits. (1a) In Maple, create a text region and enter the following

Question

Calculating limits. (1a) In Maple, create a text region and enter the following sentence: Finding two-sided limits. Insert an execution group (command prompt) after the the text region. (b) In Maple, create the function f(x) = sin(|x|)/x . ( HINT: Use sin(abs(x))/x.) (c) Plot f(x) with the x-axis varying from -10 to 10. Notice that there seems to be a jump between y = -1 and y = 1. Fix the plot by including discont = true in the plot command. (d) QUESTION: Considering the graph, GUESS the value of lim (x->0) f(x)? (e) Calculate the left-hand limit lim (x->0-) f(x)? using Maple. (f) Calculate the right-hand limit of f(x) lim(x->0+) f(x)? using Maple. (g) QUESTION: Does lim (x->0) f(x) exist? Explain your answer. (h) Confirm your answer by calculating [> limit(f(x), x=0); PLEASE NOTE(IF YOU SEE ? MARK IT ACTUALLY REPRESENTS A - (MINUS) SIGN!

Explanation / Answer

ANSWER Yes. The definition of lim(x->0) f(x) does not require that f be defined at 0. Example: f(x) = e^(-1/x^2) Then f is not defined at x=0, but lim (x->0) f(x) = 0.

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