### HOW PRE-SERVICE MATHEMATICS TEACHER PROVE THE LIMIT OF A FUNCTION BY FORMAL DEFINITION?

#### Abstract

The purpose of this study was to investigate the flow of thoughts of pre-service mathematics teacher through the answers of limit of a function evaluation by formal definition. This study used qualitative approach with descriptive method. The research subjects were students of mathematics education study program, Universitas Serang Raya. After analyzing the students’ written answers, interview was conducted to get further explanation on their strategies and common mistakes. This study found that based on the students’ results in the limit of a function evaluation by formal definition, there were common strategies, i.e. (1) preparation of proof which consisted of (a) determining delta value by the final statement of formal definition, (b) substitution process, (c) simplifying value in absolute sign, (d) solving inequality, (e) finding delta value; and (2) proving which consisted of (f) positive epsilon statement, (g) defining delta, (h) positive delta statement, (i) substitution of constants and delta values in the initial statement of formal definition, (j) solving inequality to create inequality in the final statement of formal definition.

#### Keywords

#### References

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DOI: https://doi.org/10.22342/jme.9.2.5684.%25p

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