EK 1.1C2 The limit of a function may be found by using algebraic manipulation, alternate forms of trigonometric functions, or the – squeeze theorem Misconceptions: Some of the problems that students will work in this unit are very abstract due to the fact that they are defined by an integral. A slow, methodical approach is recommended when teaching this topic. The College Board has many examples that involve analytical and graphical approaches to functions defined by integrals. Concepts/Content: Competencies/Skills: Description of Activities: reciprocal functions applying various differentiation teacher led direct instruction functions defined by integrals rules question & answer properties of logarithms applying various anti-derivative check/review HW logarithmic differentiation rules warm-up / exit ticket questions 2nd part of the Fundamental analyzing a function defined by quiz Theorem of Calculus an integral graphically problem set L’Hospital’s Rule applying the 2nd part of the FTC end-of-unit test to find derivatives of functions specific example of activity L’Hospital’s “Why defined by integrals Rule Works” activity apply L’Hospital’s Rule to evaluate limits Assessments: informal questioning quiz problem set end-of-unit test Interdisciplinary Connections: Additional Resources: N/A Foerster textbook (Kendall Hunt) sections: 6-2, 6-3, 6-4, – textbook supplemental materials (explorations) TI-89 graphing calculator, desmos.com selected MC/FR from released AP exams College Board’s AP Calculus AB course description Calculus in Motion computer simulations
EK 1.1C2 – The limit of a function may be found by using algebraic manipulation, alternate forms of trigonometric functions, or the squeeze theorem Misconceptions: Some of the problems that students will work in this unit are very abstract due to the fact that they are defined by an integral. A slow, methodical approach is recommended when teaching this topic. The College Board has many examples that involve analytical and graphical approaches to functions defined by integrals. Concepts/Content: reciprocal functions functions defined by integrals properties of logarithms logarithmic differentiation 2nd part of the Fundamental Theorem of Calculus L’Hospital’s Rule Competencies/Skills: applying various differentiation rules applying various anti-derivative rules analyzing a function defined by an integral graphically applying the 2nd part of the FTC to find derivatives of functions defined by integrals apply L’Hospital’s Rule to evaluate limits Description of Activities: teacher led direct instruction question & answer check/review HW warm-up / exit ticket questions quiz problem set end-of-unit test specific example of activity “Why L’Hospital’s Rule Works” activity Assessments: informal questioning quiz problem set end-of-unit test Interdisciplinary Connections: N/A Additional Resources: Foerster textbook (Kendall Hunt) – sections: 6-2, 6-3, 6-4, textbook supplemental materials (explorations) TI-89 graphing calculator, desmos.com selected MC/FR from released AP exams College Board’s AP Calculus AB course description Calculus in Motion computer simulations
2017-AP-Calculus-AB-BHASD-Math-Curriculum.docx