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This lecture covers the concept of infinite branches in functions defined in the neighborhood of a real number, where at least one of the limits tends to ±∞, leading to the presence of vertical asymptotes. It also explains oblique asymptotes for functions defined on [c, +∞[, where the limit tends to ±∞, and how to determine them. Examples are provided to illustrate these concepts, such as functions with oblique asymptotes when x tends to ±∞. The lecture concludes with the calculation of limits for functions involving square roots and the determination of oblique asymptotes.