While there is no single "official" student solution manual published by the textbook's author for general public release, several comprehensive community-driven and independent solution guides exist for Tom Apostol's Calculus, Volume 1
For decades, Tom M. Apostol’s Calculus, Volume 1: One-Variable Calculus, with an Introduction to Linear Algebra has held a unique, almost mythical status in the world of mathematics education. Unlike typical “calculus for engineers” textbooks that prioritize rote computation, Apostol’s masterpiece is revered for its rigor, its historical insight, and its infamous problem sets. tom apostol calculus volume 1 solutions pdf
Below are the most reliable sources for solutions to the exercises: Ernest Yeung's Solution Manual While there is no single "official" student solution