NOTES 01.1 Limits & Continuity.pdf - Calculus Maximus Notes...

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Calculus Maximus Notes 1.1: Limits & Continuity Page 1 of 11 §1.1—Limits & Continuity What do you see below?
Calculus Maximus Notes 1.1: Limits & Continuity Page 2 of 11 Example 1: (Calculator) For 2( )f xx(a) fill in the following chart x2.92.992.9993.13.013.001(fx(b) What do these values tell us about fin the neighborhood of 3x(c) Based on the chart above, what do you think is the value of (3f(d) What IS (3fExample 2: (Calculator) If 323( )3xxg xx-=-, (a) fill in the following chart x2.92.992.9993.13.013.001(g x(b) What do these values tell us about gin the neighborhood of 3x(c) Based on the chart above, what do you think is the value of (3g(d) What IS (3g(e) Is there a still a way to mathematically communicate the result from the chart above? ==? ? ? =? ? ?
Calculus Maximus Notes 1.1: Limits & Continuity Page 3 of 11
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Example 3: Suppose you wanted to safely and smooooothly cross a chasm in your car. What three things would you need? Would you be able to do so in the situation depicted in the photo to the right? What is missing? If you were to build the bridge, would you know exactly where to build it to make crossing the chasm in a car a continuously smooth undertaking?

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