Verified Certificate

Supported by the following organizations

This is to certify that Ram Mukund Kripa 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

John Wesley Cain

Senior Lecturer on Mathematics Harvard University

Juliana Belding

Juliana Belding

Professor of the Practice Boston College

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About edX Verified Certificates

An edX Verified Certificate signifies that the learner has agreed to abide by the edX honor code and completed all of the required tasks of this course under its guidelines, as well as having their photo ID checked to verify their identity.