Solving Problems in Mathematical Analysis, Part I by Tomasz Radożycki

Author:Tomasz Radożycki
Language: eng
Format: epub
ISBN: 9783030358440
Publisher: Springer International Publishing

just this one that is not defined at this point is thrown away. Always, if this kind of doubt arises, one has to think how to understand a given expression so that it makes sense.

After these considerations, one sees that for |a| > 1, the formula (8.2.19) is applicable, and thus, the conclusions are too. The function is continuous at the “gluing” points only for a = 0, which conflicts with the relevant condition |a| > 1.

In conclusion, one can write that for a = 0 the function is continuous at all points of its domain, and for a ≠ 0 (and naturally a ≠ − 1), it is discontinuous at the points x k = π∕2 + 2kπ.

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