'Approaches infinity' presentation slideshows

Problem of the Day

Problem of the Day. If f ''(x) = x(x + 1)(x - 2) 2 , then the graph of f has inflection points when x =. a) -1 only b) 2 only c) -1 and 0 only d) -1 and 2 only e) -1, 0, and 2 only. Problem of the Day. If f ''(x) = x(x + 1)(x - 2) 2 ,

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Introduction to Limits

Introduction to Limits. What is a limit?. A Geometric Example. Look at a polygon inscribed in a circle. As the number of sides of the polygon increases, the polygon is getting closer to becoming a circle. If we refer to the polygon as an n- gon ,

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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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Aim: Do Limits at Infinity make sense?

Aim: Do Limits at Infinity make sense?. Do Now:. List the characteristics of the following function. y = 3. x decreases w/o bound. x increases w/o bound. f(x) approaches 3. f(x) approaches 3. Do Now. f ( x ) ?? 3 as x ? -?. f ( x ) ?? 3 as x ? ?.

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Limits Involving Infinity

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1.5 Infinite limits

1.5 Infinite limits. "I never got a pass mark in math ... Just imagine -- mathematicians now use my prints to illustrate their books." -- M.C. Escher. Objective:. To describe infinite limits. Black holes. Start with any number

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2.2 Limits Involving Infinity

2.2 Limits Involving Infinity. As the denominator gets larger, the value of the fraction gets smaller. There is a horizontal asymptote if:. or. This number becomes insignificant as. There is a horizontal asymptote at 1. Example 1:. Find:.

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2.2 Limits Involving Infinity

2.2 Limits Involving Infinity. Finite Limits as The symbol for infinity does not represent a real number. We use infinity to describe the behavior of a function when the values in its domain or range outgrow all finite bounds.

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The Nature of Graphs - Ch 03

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2.2 Limits Involving Infinity

Photo by Vickie Kelly, 2006. Greg Kelly, Hanford High School, Richland, Washington. 2.2 Limits Involving Infinity. North Dakota Sunset. As the denominator gets larger, the value of the fraction gets smaller. There is a horizontal asymptote if:. or.

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Vertical Asymptote

Vertical Asymptote. If f ( x ) approaches infinity (or negative infinity) as x approaches c from the right or the left, then the line x = c is a vertical asymptote of the graph of f. Infinite Limits. The limit statement such as

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Infinite Limits

Infinite Limits. Lesson 2.5. Previous Mention of Discontinuity. A function can be discontinuous at a point The function goes to infinity at one or both sides of the point, known as a pole Example Enter this function into the Y= screen of your calculator Use standard zoom.

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Graphing Polynomials

Graphing Polynomials. Determine degree End behavior Number of Zeros Turning points Find the zeros and determine behavior at zero Find the y-intercept and a few other points.

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Calculus Chapter One

Calculus Chapter One . Sec 1.5 Infinite Limits. Sec 1.5. Up until now, we have been looking at limits where x approaches a regular, finite number. But x can also approach ? or -?. Limits at infinity exist when a function has a horizontal asymptote. Sec 1.5.

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INFINITE LIMITS (1.5)

September 11th, 2017. INFINITE LIMITS (1.5). I. INFINITE LIMITS.

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is an unbiased estimate of .

is an unbiased estimate of . Consider the following data matrix. Note that To obtain the mean squared deviation of each observation in the data matrix about the grand mean of all observations, we may proceed as follows:

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