Solution IDZ Ryabushko 5.2 - Option 5

Section: Chapter 5. Functions. Limits. Continuity of functions
Topic: Comparison of infinitesimals. Continuity of functions
Description: Comparison of infinitesimal functions, determination of the order of smallness. Using equivalent infinitesimals to calculate limits. Investigation of functions for continuity, classification of discontinuity points, construction of graphs.

Quests:
1. Prove that functions f(x) and φ(x) as x→0 are infinitesimals of the same order of smallness.
2. Find the limits using equivalent infinitesimal functions.
3. Investigate the given functions for continuity and construct their graphs.
4. Investigate the given functions for continuity at the specified points.

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