AP Calculus Desmos File Library
Tables of Points
TABLE OF POINTS to approximate a limit at x = n
  • this is a file that the user can modify to investigate limits using tables as they approach a particular function value of a particular value of x
  • The default function actually cannot have its limit determined at x = 0 using this method because there is an oscillating function
    • f(x)=x sin(1/x)
  • This particular limit as x approaches 0 requires the Squeeze Theorem
    • some call the Squeeze Theorem the Sandwich Theorem too!
  • DESMOS File
Limits
Find Limits Using a Table
  • This is a template document for a specific set of homework, but it can easily be modified to investigate a particular value of x on a function
  • DESMOS Link
Find Limits Using a Graph
  • This is a template document for a specific set of homework, but it can easily be modified to investigate a particular value of x on a function
  • DESMOS Link
  • The default example is an example of a function that DOES NOT have a limit because of a oscillating discontinuity at x = 0
    • f(x)=sin(1/x)

Piecewise Functions 
FIVE PIECE Piecewise Function Template Document
  • this allows the user to change some commonly used functions in a piecewise function
    • line
    • standard form parabola
    • square root in translated form
    • absolute value function in translated form
    • tangent function
  • This template document allows the users to define the piecewise functions endpoints 
  • This template allows the users to define the function value at end points
  • DESMOS File
SIX PIECE Piecewise Function Template Document
  • this allows the user to change some commonly used functions in a piecewise function
    • line
    • standard form parabola
    • square root in translated form
    • absolute value function in translated form
    • tangent function
    • sine function
  • This template document allows the users to define the piecewise functions endpoints 
  • This template allows the users to define the function value at end points
  • DESMOS File

Rates of Change

Tangents and Normals

Derivatives

Integrals 

Area under Curve

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