Limits_and_Differentiation

# Limits_and_Differentiation - Vineet Goyal Limits Continuity...

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QSRP - Chapter 10 1 Vineet Goyal Continuity Limits Derivative Rules Log.,Exp. Functions Implicit Differentiation Quantitative Skills Review Program Chapter 10

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QSRP - Chapter 10 2 Vineet Goyal Continuity Limits Derivative Rules Log.,Exp. Functions Implicit Differentiation Limits Get “closer and closer” to a value yet never “touch” it Usually want to study how functions behave as you get close to forbidden values Example from notes
QSRP - Chapter 10 3 Vineet Goyal Continuity Limits Derivative Rules Log.,Exp. Functions Implicit Differentiation Limits Definition (pg. 450 of text) The limit of f(x) as x approaches a is the number L, provided that f(x) is arbitrarily close to L for all x sufficiently close to , but not equal to a. Example Walk from A to B covering half the distance at each step Example when limit (as x -> a) is not defined (case) A B

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QSRP - Chapter 10 4 Vineet Goyal Continuity Limits Derivative Rules Log.,Exp. Functions Implicit Differentiation Obtaining Limits By factoring and cancellation Example 7, pg. 455 of text 0/0 Example 9, pg. 456 of text Special limit Pg. 456 of text One-sided limits, Limits at infinity Pg 458 and 460 of text
QSRP - Chapter 10 5 Vineet Goyal Continuity Limits Derivative Rules Log.,Exp. Functions Implicit Differentiation Continuity Defn: A function f is continuous at a iff (i) f(x) defined at x = a (ii) lim x->a f(x) exists and is equal to f(a) Example Figures 10.23, 10.24, pg. 466 of text Polynomial functions are continuous at every point

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QSRP - Chapter 10 6 Vineet Goyal Continuity Limits Derivative Rules Log.,Exp. Functions Implicit Differentiation End of Chapter 10 Read Mathematical Snapshot, p. 478
QSRP - Chapter 10 7 Vineet Goyal Continuity Limits Derivative Rules Log.,Exp. Functions Implicit Differentiation Quantitative Skills Review Program Differentiation Chapters 11 and 12

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QSRP - Chapter 10 8 Vineet Goyal Continuity Limits Derivative Rules Log.,Exp. Functions
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## This note was uploaded on 10/05/2010 for the course BUS 1142 taught by Professor Miller during the Fall '10 term at Carnegie Mellon.

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Limits_and_Differentiation - Vineet Goyal Limits Continuity...

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