From textbook we have the following results[br][img]data:image/png;base64,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[/img][br]How can we verify them with the applet?
What happens to the limit for negative values of a?
(a) Set a = 1.1 then connect points with function1, guess what is function1?[br](b) Why function1 disappear for negative a?[br](c) For negative a, connect points with function2, guess what is function2?[br](d) Does function2 pass through all the points for any a?[br](e) Guess how we define function3.