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 MAT 145

Wednesday, January 16, 2019 MAT 145

Secant-line Slopes to Tangent-line Slope Wednesday, August 22, 2018 MAT 145

Wednesday, August 22, 2018 MAT 145

Wednesday, January 16, 2019 MAT 145

Wednesday, January 16, 2019 MAT 145

Wednesday, January 16, 2019 MAT 145

Wednesday, January 16, 2019 MAT 145

Wednesday, January 16, 2019 MAT 145

Wednesday, January 16, 2019 MAT 145

Wednesday, January 16, 2019 MAT 145

Wednesday, January 16, 2019 MAT 145

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 MAT 145

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 MAT 145

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 MAT 145

Approachment Wednesday, January 16, 2019 MAT 145

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 MAT 145

“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 MAT 145

Change, Change, Change! Wednesday, January 16, 2019 MAT 145

Change, Change, Change! Wednesday, January 16, 2019 MAT 145

Change, Change, Change! Wednesday, January 16, 2019 MAT 145

Accumulate, Accumulate, Accumulate! How much snow fell? Wednesday, January 16, 2019 MAT 145

Accumulate, Accumulate, Accumulate! How much snow fell? Wednesday, January 16, 2019 MAT 145

Accumulate, Accumulate, Accumulate! How much snow fell? Wednesday, January 16, 2019 MAT 145

Wednesday, January 16, 2019 MAT 145

Making Connections CHANGE ACCUMULATE CALCULUS! PRE-CALCULUS! LIMITS FUNCTIONS ACCUMULATE PRE-CALCULUS! Wednesday, January 16, 2019 MAT 145

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 MAT 145

Wrapping It Up Admin Details Course Resources Assignments Syllabus Expectations Course Resources Textbook WebAssign Calculators Course Website: math.illinoisstate.edu/day/courses/current/145/www.html Assignments Handout: Tasks #3 -#5 Sec 2.1 mirrors today’s activities. Wednesday, January 16, 2019 MAT 145