Calculus Homework: Limits, Continuity, and Derivatives

This document presents a comprehensive solution to a calculus assignment. The assignment includes detailed solutions to problems involving limits, continuity, and derivatives. Question 1 evaluates various limits using techniques such as L'Hopital's rule and conjugate multiplication. Question 2 discusses the continuity of a function and analyzes the roots of a related function, while Question 3 focuses on making a variable the subject of a formula and solving for it. Question 4 finds vertical and horizontal asymptotes. Question 5 explores the behavior of a function, identifying critical and inflection points, and determining concavity. Question 6 involves evaluating definite integrals, and Question 7 further explores integration techniques. The solutions are presented step-by-step, providing a clear understanding of the concepts and methods used.