calculus chapter 1 - Chapter 1: Limits and Continuity 1.1...

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Chapter 1: Limits and Continuity 1.1 Examples of Velocity, Growth Rate, and Area -Average Velocity = Change of Position Amount of Time -Instantaneous Velocity= lim f(t+h) – f(t) h->0 h -Average Rate of Growth= Change in Growth = slope of line joining the points of Time the graph -instantaneous Growth: measure average rates of change over shorter times and a tangent line is drawn and the slope of that line is found 1.2 Limits of Functions Limit: If f(x) is defined for all x near a, except possibly at a itself, an if we can ensure that f(x) is as close as we want to L by taking x close enough to a, but not equal to a, we say that the function f approaches the limit L as x approaches a Lim f(x) = L x->a -left limit: if f(x) is defined on some interval (b,a) extending to the left of x=a, and if we can ensure that f(x) is as close as we want to L by taking x to the left of a and close enough to a, then we say f(x) has left limit L at x=a -right limit: if f(x) is defined on some interval (a,b) extending to the right of x=a, and if we can ensure that f(x) is as close as we want to L by taking x to the right of a and close enough to a, then we say f(x) has right limit L at x=a. Theorem 1: lim f(x) = L
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This note was uploaded on 03/03/2010 for the course CALC 1110 at Cornell University (Engineering School).

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calculus chapter 1 - Chapter 1: Limits and Continuity 1.1...

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