1. Calculus I (MAT 145) Dr. Day Wednesday January 16, 2019
Secant-line Slopes to Tangent-line Slope
Numerical Approximation: We’ve shown and practiced this.
Graphical Approximation: Accurate scales will produce useful results.
Algebraic Representation: Exact Value! There’s a hitch, however . . .
Approachment: Looking for Patterns
Quiz #1 today
Tasks 3, 4, 5 on Secant-line Slopes to Tangent-line Slope Handout
Friday: Quiz #2
Wednesday, January 16, 2019
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2. Wednesday, January 16, 2019
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3. Secant-line Slopes to Tangent-line Slope
Wednesday, August 22, 2018
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4. Wednesday, August 22, 2018
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5. Wednesday, January 16, 2019
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6. Wednesday, January 16, 2019
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7. Wednesday, January 16, 2019
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8. Wednesday, January 16, 2019
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9. Wednesday, January 16, 2019
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13. Approachment
As the values of some set of inputs tend to get closer and closer to a number, the corresponding list of outputs get closer and closer to some number.
Wednesday, January 16, 2019
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14. Approachment
As the values of some set of inputs tend to get closer and closer to a number, the corresponding list of outputs get closer and closer to some number.
The set of x values; values in the domain of some function
approach
Some specific number, may or may not be in the domain of the function
The set of function outputs; values in the range of some function
approach
Some specific number, may or may not be in the range of the function
Wednesday, January 16, 2019
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15. Transitioning from . . . Approachment
As the values of some set of inputs tend to get closer and closer to a number, the corresponding list of outputs get closer and closer to some number.
… to … an equivalent
mathematical representation
Wednesday, January 16, 2019
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16. Approachment
Wednesday, January 16, 2019
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17. The concept of LIMIT!
This says that the values of f(x) tend to get closer and closer to the number L as x gets closer and closer to the number a (from either side of a) regardless of the value of f(a).
Wednesday, January 16, 2019
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18. “The limit of f(x), as x approaches a, is L.”
The concept of LIMIT!
“The limit of f(x),
as x approaches a,
is L.”
Wednesday, January 16, 2019
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19. Change, Change, Change!
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20. Change, Change, Change!
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21. Change, Change, Change!
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22. Accumulate, Accumulate, Accumulate!
How much snow fell?
Wednesday, January 16, 2019
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23. Accumulate, Accumulate, Accumulate!
How much snow fell?
Wednesday, January 16, 2019
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24. Accumulate, Accumulate, Accumulate!
How much snow fell?
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25. Wednesday, January 16, 2019
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26. Making Connections CHANGE ACCUMULATE CALCULUS! PRE-CALCULUS! LIMITS
FUNCTIONS
ACCUMULATE
PRE-CALCULUS!
Wednesday, January 16, 2019
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27. Algebra Will Get You Every Time
Expanding and Factoring, Reducing Fractions, and Other Ways to Simplify Expressions
Solving Equations
Functions and Their Properties
Linear Functions, Other Polynomial Functions, Exponential Functions, Logarithmic Functions, Rational Functions, Trig Functions, and Others
Domain and Range, Asymptotes, Increasing and Decreasing Intervals, Extreme Values, End Behavior
Wednesday, January 16, 2019
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28. Wrapping It Up Admin Details Course Resources Assignments Syllabus
Expectations
Course Resources
Textbook
WebAssign
Calculators
Course Website: math.illinoisstate.edu/day/courses/current/145/
Assignments
Handout: Tasks #3 -#5
Sec 2.1 mirrors today’s activities.
Wednesday, January 16, 2019
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