'Function approaches' diaporamas de présentation

Limits of Functions

Limits of Functions.

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2.1 Rates of Change & Limits

2.1 Rates of Change & Limits. Average Speed. Average Speed. Since d = rt ,. Example: Suppose you drive 200 miles in 4 hours. What is your average speed?. = 50 mph. Instantaneous Speed. The moment you look at your speedometer, you see your instantaneous speed. Example

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Consider the integral:

Consider the integral:. t = 2. t = 3. t = 5. ?. Example:. Example:. The function is undefined at x = 1. Since x = 1 is an asymptote, the function has no maximum. We could define this integral as:. Can we find the area under an infinitely high curve?. (left hand limit).

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LIMITS

LIMITS. Chris Floyd Zach Hilley Aaron Hevenstone. LIMITS. A LIMIT IS THE VALUE A FUNCTION APPROACHES AT A CERTAIN POINT. Is it continuous?. Functions can have continuities, discontinuities, or even bothinuities.

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The Limit of a Function

Photo by Vickie Kelly, 2007. Greg Kelly, Hanford High School, Richland, Washington Adapted by: Jon Bannon, Siena College. The Limit of a Function. Grand Teton National Park, Wyoming. Then your average speed is:. Suppose you drive 200 miles, and it takes you 4 hours.

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2.1 Rates of Change and Limits

Photo by Vickie Kelly, 2007. Greg Kelly, Hanford High School, Richland, Washington. 2.1 Rates of Change and Limits. Grand Teton National Park, Wyoming. Then your average speed is:. Suppose you drive 200 miles, and it takes you 4 hours.

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2.1 Rates of Change and Limits

2.1 Rates of Change and Limits. Then your average speed is:. Suppose you drive 200 miles, and it takes you 4 hours. If you look at your speedometer during this trip, it might read 65 mph. This is your instantaneous speed. A rock falls from a high cliff.

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The Nature of Graphs - Ch 03

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GISAT 151 (Week 4a)

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2.6 Rational Functions

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2.6 Rational Functions

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Continuity, End Behavior, and limits

Continuity, End Behavior, and limits. COntinuity. A continuous function has no breaks, holes, or gaps You can trace a continuous function without lifting your pencil. Types of Discontinuity. Infinite (non-removable)

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Lesson 2-7: Graphing Rational Functions

Lesson 2-7: Graphing Rational Functions. Advanced Math Topics. Definitions. Continuity: a graph that is able to be traced without picking up the pencil Asymptote: a line that the graph of the function approaches, but never touches (graphed as a dotted line)

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2.2 Limits

2.2 Limits. Definition of Limit: Suppose that f(x) becomes arbitrarily close to the number L ( f(x) ? L ) as x approaches a ( x ? a ). Then we say that the limit of f(x) as x approaches a is L and write. Note 1: The number a may be replaced by ?. 1. Example 1:

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Bell Ringer 10-26-16

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Introduction to Limits, Continuity , and End Behavior

Introduction to Limits, Continuity , and End Behavior. Honors Precalculus Functions Mr. Frank Sgroi , M.A.T. Holy Cross high School.

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2-1 Rates of Change and Limits

2-1 Rates of Change and Limits. Average vs. Instantaneous Speed Position function ? f ( t ) time ? t time interval ? h Average speed. Ex 1) A rock breaks loose from the top of a cliff. What is the average speed during the first 2 seconds of fall?. h.

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Limits Graphically

Limits Graphically. TS: Explicitly assessing information and drawing conclusions. Warm Up: Find the following limit using whatever means you can. Objective. To find the limit of a function by examining its graph. Limits Graphically. 6. 6. 6. 6. Limits Graphically. Undefined. 2. 2.

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