Key Types of Questions: Limits and Derivatives - Common Calculus Exam Problem Analysis
The concept of limits is the foundation of calculus and serves as the crucial bridge connecting differentiation and integration. This unit will focus on the computation of limits and how to use limits to find derivatives, differential functions, and asymptotes. Table of Contents Precise Definition of Limits Limits of Composite Functions Squeeze Theorem Definition of Derivatives Finding Asymptotes Precise Definition of Limits Do not underestimate this concept. In high school, we learn an intuitive definition of limits, but the college definition is different and often a focal point for professors. Here’s a review of the precise definition of limits: We write lim if for every number \delta \gt 0 there is a number \varepsilon \gt 0 such that \(\bbox[#e0ebeb,5px,border:3px solid #b3f0ff]{\text{if}~0<\left|x-a\right|<\delta~~~ \text{then}~~ \left|f(x)-L\right|...