Supported by the following organizations
This is to certify that Marcos Rodrigues Barreto successfully completed and received a passing grade in CalcAPL1x: Calculus Applied! a course of study offered by HarvardX, an online learning initiative of Harvard University.
Noted by
John Wesley Cain
Senior Lecturer on Mathematics Harvard University
Juliana Belding
Professor of the Practice Boston College
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- Verified Certificate Issued September 7, 2026
- Valid Certificate ID df4e4deda84f47f0a11a93556e0e493c