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This book titled “Real Analysis (Volue-3)” is a continuation of Real Analysis (Volume-1) and (Volume-2). It is designed for UG and PG students of mathematics to understand the underlying principles and essence of real analysis. To achieve them authors have given detailed proofs for theorems and detailed solutions of a large number of problems on each topic. The main aim of this book is a student can learn its content through his self-study. This book consisting of six chapters Mean value theorems, Taylor’s and Maclaurin’s expansion, indeterminate forms, Riemann integration, Riemann-Stiljes integration and improper integrals.