Approximating limits using tables | Limits and continuity | AP Calculus AB | Khan Academy | Summary and Q&A

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September 11, 2017
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Approximating limits using tables | Limits and continuity | AP Calculus AB | Khan Academy

TL;DR

Analyzing the limit of a function as x approaches three to determine its value.

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Questions & Answers

Q: What happens to the expression when x equals three?

When x equals three, the expression results in an indeterminate form of zero over zero, as both the numerator and denominator become zero.

Q: Why are two tables set up for approximation?

Two tables are set up to estimate the limit from both sides of three - values less than three (from the left) and values larger than three (from the right). This ensures that both approaches converge to the same value for the limit.

Q: Is the limit from the left negative values?

No, the limit from the left refers to values less than three, approaching three from the left side. It does not necessarily involve negative values, but rather values closer to three from the left side.

Q: How is the limit estimate calculated?

The limit estimate is calculated by plugging in x values closer and closer to three into the expression and observing the resulting values. Based on this, an estimation is made for the value that the limit approaches.

Summary & Key Takeaways

  • The expression x to the third power minus three times x squared over five times x minus 15 is not defined when x equals three, as it results in an indeterminate form of zero over zero.

  • To estimate the limit of the expression as x approaches three, two tables are set up: one for values less than three (from the left) and one for values larger than three (from the right).

  • By calculating the expression for values closer to three, it is estimated that the limit approaches 1.8.

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