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At the top of a new Maple worksheet type the following lines in a text region;

Maple Lab 4: Limits of Functions

1) Calculating limits.

(a) 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);

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