Calculus Syllabus

Subject

CALCULUS/STATISTICS

 

Nine Week

 

Q1

Standard

 

 

 

 

 

  • Calculate limits using algebra
  • Estimate limits of functions from graphs or tables of data. Apply the definition of a limit to a variety of functions, including piece-wise functions.
  • Draw a sketch that illustrates the definition of the limit, develop multiple real world scenarios that illustrate the definition of the limit
  • Describe asymptotic behavior in terms of infinite limits and limits at infinity.
  • Discuss the various types of end behavior of functions, identify prototypical functions for each type of end behavior.
  • Define continuity at a point using limits, define continuous functions.
  • Determine whether a given function is continuous at a specific point.
  • Determine and define different types of discontinuity in terms of limits
  • Apply the Intermediate Value Theorem and Extreme Value Theorem to continuous functions.

 

Objectives

 

 

 

 

 

 

 

 

 

  • Determine continuity at a point and continuity on a closed interval.
  • Determine one-sided limits and continuity on a closed interval.
  • Use properties of continuity.
  • Understand and use the Intermediate Value Theorem.
  • Determine infinite limits from the left and from the right.
  • Find and sketch the vertical asymptotes of the graph of a function.
  • Determine llimits at infinity.
  • Determine the horizontal asymptotes of the graph of a function.
  • Find the slope of the tangent line to a curve at a point
  • Use the liit definition to find the derivative of a function.
  • Understand the relationship between differentiability and continuity.

 

Topics

 

 

 

 

 

  • Prerequisite review of algebraic functions, difference quotient, graphing, trigonometry
  • Functions and modeling
  • Limits and derivatives
  • Differentiation rules

 

 

 

Major Assignment/s

 

 

 

 

 

 

  • 9 weeks exam
  • 6 chapter exams
  • 12 quizzes

 

Instructional Materials

 

  • CALCULUS EARLY TRANSCENDENTALS 7E, BY JAMES STEWART textbook
  • TI 84 GRAPHING CALCULATOR

 

 

Field Trip/s

 

none

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