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Limits, Asymptotes, and Continuity Ex.
Def. A horizontal asymptote of f (x) occurs at y = L if or Def. A vertical asymptote of f (x) occurs at values of x where f (x) is undefined (sort of). and are examples of graphs that have a hole.
Ex. Find all asymptotes of, then sketch the graph.
means that x approaches 2 from the right (larger than 2) means that x approaches 2 from the left (smaller than 2) One-Sided Limits Ex.
Thm. The limit exists if both sides agree.
Ex. For the function given, find: a. b. c.
Ex. Find if
Def. (loose) A function is continuous on an interval if the graph has no gaps, jumps, or breaks on the interval. Ex. Is continuous on [0,5]?
Def. (tight) A function f (x) is continuous on an interval if, for all points c on the interval: i. exists ii. exists iii.
Ex. Let Find a value of B so that f (x) is continuous at x = 0.
The test on Chapter 1 will be on Monday. Next class we will review and Ill pass out a Sample Test so you know what types of questions I can ask.
I can solve limits involving infinity.
9.3 Rational Functions and Their Graphs
Graph of Exponential Functions
HYPERBOLAS The equation of a hyperbola is almost exactly that of an ellipse. The only change that occurs is there is a minus sign between the terms. ALSO,
Q2-1.1a Graphing Data on the coordinate plane
The derivative and the tangent line problem (2.1) October 8th, 2012.
Objective: Sketch the graphs of tangent and cotangent functions.
Good Morning, Precalculus! When you come in, please Grab your DO NOW sheet 2. Place the homework that was due today at the front of your desk: Pg.
Concavity & the second derivative test (3.4) December 4th, 2012.
LESSON 5 Section 6.3 Trig Functions of Real Numbers.
Graphs of Exponential and Logarithmic Functions
Chapter 3 Limits and the Derivative
Extrema on an interval (3.1) November 15th, 2012.
Slopes of Lines Chapter 3-3.
ACT Class Openers:
ACT Class Opener: om/coord_1213_f016.htm om/coord_1213_f016.htm
Point of Discontinuity
Objectives: 1.Be able to define continuity by determining if a graph is continuous. 2.Be able to identify and find the different types of discontinuities.
Limit & Derivative Problems Problem…Answer and Work…
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