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Problems > Mr. T's Calculus > 2006

Testing the Limits

Find the following limit algebraically. In your solution, describe the process used. Do NOT simply plug the expression into a grapher to find the limit.

lim
x3 - 7x + 6
x3 - 39x + 70
x→2

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What's the area?

A certain lake has an irregular shape. In order to estimate the area, the North-South distance across the lake is measured every 100 feet down an East-West line. The results are shown in the table below. Use an appropriate technique to estimate the number of acres that the lake covers. Give a complete explanation of how you computed the area.
East-West position (ft) Distance across lake (ft)
0 900
100 1500
200 1800
300 2000
400 2500
500 2700
600 2700
700 2700
800 2700
900 2700
1000 2700
1100 2700
1200 2700
1300 2700
1400 2600
1500 2600
1600 2600
1700 2600
1800 2600
1900 2600
2000 2500
2100 2500
2200 2500
2300 2500
2400 2500
2500 2500
2600 2400
2700 2300
2800 2300
2900 1800
3000 1600
3100 1500
3200 1400
3300 1400
3400 1300
3500 1300
3600 1100
3700 800
3800 0
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