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Section 2.2 The Limit of a Function AP Calculus September 10, 2009 CASA
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Calculus, Section 2.22 “Calculus Close” In calculus, we will continually look at what happens in very small intervals. The book uses the term “arbitrarily close” to describe a situation where we are close enough to see what is at a point, but not actually at that point Mr. Pierce, calculus teacher at Buffalo Grove High School (IL), calls this “calculus close”
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Calculus, Section 2.23 Definition of Limit “The limit of f of x as x approaches a.” The limit of a function is the value of the function as it approaches, but does not reach it’s destination.
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Calculus, Section 2.24 Situation 1 Situation 1: Function is continuous at the point in question. The limit of f(x) as x approaches 2 is 4 Also, f(2)=4 (The function is continuous at 2)
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Calculus, Section 2.25 Situation 2 Function has a hole (the function is not continuous) and both sides of the function approaches the empty spot.
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Calculus, Section 2.26 Situation 3 The function is not continuous, both sides of the function does not approach the hole. We say the limit exists when approaching from the left (-), exists when approaching from the right (+), but the limit DOES NOT EXIST (DNE)
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Calculus, Section 2.27 Situation 4.1 When function has a vertical asymptote, we say the “limit of the function approaches infinity.” a b c
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Calculus, Section 2.28 Situation 4.2 If the left-hand limit does not agree with the right-hand limit, we say the limit does not exist. a b c
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Calculus, Section 2.29 Situation 4.3 When function has a vertical asymptote, we say the “limit of the function approaches infinity.” a b c
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Calculus, Section 2.210 Definition of a Vertical Asymptote If has a vertical asymptote at at least one of these statements is true
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Calculus, Section 2.211 Using the TI-83 (trends)
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Calculus, Section 2.212 Using the TI-83 (warnings)
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Calculus, Section 2.213 Using the TI-83 (warnings)
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Calculus, Section 2.214 Assignment Section 2.2, 1-39 odd
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