Making sense of mathematical expressions is a central component of expert-like reasoning in physics. Previous research has shown that sensemaking strategies can be successfully integrated into university instruction and that students benefit from explicit support in using such strategies. However, it remains largely unexplored to what extent the amount of practice influences students’ learning. In the present study, we investigate dose-effect relationships for sensemaking tasks with limiting case analysis. The study was conducted during a two-week {preparatory} course for incoming undergraduate physics students at a German university. The course focuses on the repetition of important mathematical concepts and prepares students for the demands of the first semester of physics studies. Limiting case analysis was systematically embedded in daily exercises that students solved in recitation sessions. A total of $N=103$ students participated in the study and were randomly assigned to one of five intervention groups, each with a different number of limiting case tasks (0-8 tasks). The study employed a pre-post design to assess perceived usefulness, instructional integration, competence, and performance regarding the analysis of limiting cases. The results show that students’ perceived competence increased with the number of tasks, with effect sizes up to $d=0.88$. Students’ performance also showed an increase in effect size for a greater number of tasks with effect sizes up to $d=1.07$. The observed patterns in the target variables are compatible with a sigmoidal dose-effect relationship. Overall, this proof-of-concept study provides first empirical evidence for dose-effect relationships in the context of sensemaking strategies in physics, and demonstrates the feasibility of dose-effect study designs in undergraduate physics education research. The study highlights the importance of explicitly integrating sensemaking strategies into undergraduate physics and indicates that increased and targeted practice can foster both students’ confidence and their ability to apply such strategies.