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1.4. The Idea of ‘Limits’. Average velocities over time:. “Instantaneous” velocity at one moment in time:. Limit of the Average velocity = the Instantaneous velocity:. The Secant approaches the Tangent (average velocity) (instantaneous velocity). 1.5.

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## The Idea of ‘Limits’

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**1.4**The Idea of ‘Limits’**Limit of the Average velocity = the Instantaneous**velocity: The Secant approaches the Tangent (average velocity) (instantaneous velocity)**1.5**The Limit of a Function**Example**Table**The limit exists if and only if “left” limit =**“right” limit**Example where limit does not exist: “Jump” behavior**As x → 2: Left limit? Right limit?**Example where limit does not exist: undefined behavior near**0**Infinite Limits**(When x approaches a number, f(x) approaches infinity)**or**Limits at Infinity (x approaches infinity, f(x) approaches a finite limit L, or infinity)

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