PPT-Limits, Continuity, Basic Differentiability, and Computing Derivati

ves By Sameer Snigdha Aditya Limits Recall that A limit is when a function gets super close to a number from both sides of x but the function never reaches that number Its predicting a number between two neighboring points. Abstract.Inthispaper,byusinggm-closedsets[27],weobtaintheunieddenitionsandpropertiesforg-continuity,gs-continuity,gp-continuity,g-continuity,\rg-continuityandgsp-continuity.2000MathematicsSubjectCl Differentiability. A function is differentiable at point . c . if and only if. the derivative from the left of . c. equals the derivative from the right of . c. .. AND. if . c. is in the domain of . Objective: Understand the relationship between differentiability and continuity. Miss . Battaglia. BC Calculus. Differentiability & Continuity. Alternative limit form of the derivative:. provided this limit exists. Note the limit in this alternative form requires that the one-sided limits. Chapter 3.2. How . Might Fail to Exist.  . A function will not have a derivative at a point . where the slopes of the secant lines . fail to approach a limit as . Some of the common ways where a function fails to have a derivative:. Ex. 1. Determine whether each function is continuous at the given . x. value(s). Justify using the continuity test. If discontinuous, identify the type of discontinuity as . infinite, jump, . or. Objective: Determine continuity at a point and on an open interval; determine one-sided limits and continuity on a closed interval.. Miss . Battaglia. AB/BC Calculus. What does it mean to be continuous?. Unit 1 Day 4. Continuity at a . POINT. A function is continuous at . a. if. . There are 3 important parts to this definition:. . f(a) . exists. The . exists (which means . =. ).. The two values above are equal.. Objective: Determine continuity at a point and on an open interval; determine one-sided limits and continuity on a closed interval.. Miss . Battaglia. AB/BC Calculus. What does it mean to be continuous?. Section 2.1. Rates of Change and Tangents . Lines to . Curves. Section 2.2. Limit of a Function. and Limit Laws. Section 2.3. The Precise Definition of a Limit. Section 2.4. One-Sided Limits. Geometrically, this means that there is NO gap, split, or missing pt. (hole) for f(x) at c.. A pencil could be moved along the graph of f(x) through (c, f(c)) WITHOUT lifting it off of the graph.. The function not only intended to reach a certain height (limit) but it actually did:. How does it apply to me?. Presented to ARMA Arizona March 2017. MHA CONSULTING, INC.. A 17-year proven track record of applying industry standards and best practices across a diverse pedigree of clients.. TOOLKIT. AND . RESOURCES. What is COOP/COG. Continuity of Operations (COOP). Continuity of Government (COG). The overall purpose of . both. . Continuity of Operations. and . Continuity of Government. are . Continuous. Connecting Differentiability . and . Continuity. Differentiability and Continuity. Continuous functions . are . not necessarily differentiable. . For instance, start with . TOLERANCES. Tolerance. . is the total amount that a specific dimension is permitted to vary in positive or negative side. It is the difference between the maximum and the minimum limits for the dimension..