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2.1 – Rates of Change and Tangents to Curves

2.1 – Rates of Change and Tangents to Curves. Function Review. 2.1 – Rates of Change and Tangents to Curves. Function Review. 2.1 – Rates of Change and Tangents to Curves. Function Review. Pascal’s Triangle. 2.1 – Rates of Change and Tangents to Curves. R ate of change:.

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2.1 – Rates of Change and Tangents to Curves

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  1. 2.1 – Rates of Change and Tangents to Curves Function Review

  2. 2.1 – Rates of Change and Tangents to Curves Function Review

  3. 2.1 – Rates of Change and Tangents to Curves Function Review Pascal’s Triangle

  4. 2.1 – Rates of Change and Tangents to Curves Rate of change: describes how one quantity changes in relation to another quantity changing. Examples: Rate: how distance changes as timechanges / / Rate: how area changes as timechanges / / Rate: how volume changes as timechanges Rate: how y changes as xchanges

  5. 2.1 – Rates of Change and Tangents to Curves Secant Line: A line joining two points on a curve. Secant line Secant line     Secant line tangent line   

  6. 2.1 – Rates of Change and Tangents to Curves Tangent Line: A line that touches a curve a one point. tangent line 

  7. 2.1 – Rates of Change and Tangents to Curves Rate of Change of a Secant Line or the Slope of a Secant Line Secant line  

  8. 2.1 – Rates of Change and Tangents to Curves Average Rate of Change Secant line   Example:

  9. 2.1 – Rates of Change and Tangents to Curves Average Rate of Change Secant line   Example:

  10. 2.1 – Rates of Change and Tangents to Curves Instantaneous Rate of Change or the Slope of a Tangent Line Secant line Secant line     Secant line tangent line   

  11. 2.1 – Rates of Change and Tangents to Curves Instantaneous Rate of Change or the Slope of a Tangent Line Secant line        

  12. 2.1 – Rates of Change and Tangents to Curves Instantaneous Rate of Change or the Slope of a Tangent Line Slope formula requires two points. A tangent line has one point on the curve. Create a second point by selecting a small value of h. tangent line 

  13. 2.1 – Rates of Change and Tangents to Curves Instantaneous Rate of Change or the Slope of a Tangent Line

  14. 2.2 – Limit of a Function and Limit Laws Defn: Limit As the variable x approaches a certain value, the variable y approaches a certain value. Find the requested limits from the graph of the given function.

  15. 2.2 – Limit of a Function and Limit Laws Given the following graph of a function, find the requested limit.

  16. 2.2 – Limit of a Function and Limit Laws Given the following graph of a function, find the requested limits.

  17. 2.2 – Limit of a Function and Limit Laws Find the requested limits for the given function.

  18. 2.2 – Limit of a Function and Limit Laws A rational function is the ratio of two polynomial functions Substitution Theorem: If f(x) is a polynomial function or a rational function, then or . If f(x) is a rational function, then the denominator cannot equal zero.

  19. 2.2 – Limit of a Function and Limit Laws

  20. 2.2 – Limit of a Function and Limit Laws Additional Limit Rules Identity Function Constant Function

  21. 2.2 – Limit of a Function and Limit Laws

  22. 2.2 – Limit of a Function and Limit Laws Find the following limits:

  23. 2.2 – Limit of a Function and Limit Laws Find the following limits:

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