Notes Limits Day 1.notebook
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Chapter 12 Limits An Intro to Calculus (12.1,12.2)
Limit fundamental concept of Calculus If f(x) becomes arbitrarily close to a unique #L as x approaches c from either side, the limit of f(x) as x approaches c is L.
Can use a table to estimate the limits: 1.
2.
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The existence or nonexistence of f(x) when x = c has no bearing on the existence of the limit of f(x) as x approaches c
Can use a graph to find the limits:
1.
Limit of a Piecewise function: 2.
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A Few Properties: Limit of a constant = constant Limit of a sum/diff = the sum/difference of limits Limit of a product/quotient = the product or quotient of the limits
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Techniques for Evaluating Limits: 1. Direct Substitution: polynomial function rational function such that q(c) ≠ 0
ex.
ex.
2. Dividing Out Tecnique: Factor and simplify, then use direct substitution
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3. Rationalizing Technique: (Rationalize the numerator)
ex.
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4. OneSided Limits with Piecewise Functions ***If f is a function and c and L are real #s, then if and only if both the left and right limits exist and are equal to L.
ex.
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Limits that fail to exist: 1. approaches two different values from the left and right 2. unbounded behavior (vertical asymptotes) ex.
3. oscillating behavior bounces between two fixed values ex.
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Homework: pg. 813814 #721 odd (do not have to construct table by hand, use calculator)
pg. 824825 #19 odd, 1323 odd, 3337 odd
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