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When would linear extrapolation be more useful than linear interpolation?

Answer 1

Some definitions first:
Linear interpolation : finding a point between two known data points under the assumption that the domain and range are linked by some linear function.

Linear extrapolation : finding a point beyond the known set of data points.

As the second example shows, linear extrapolation can be used by establishing a tangent line to the last known data point even when the data points are non-linear.

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Answer 2

Isaiah Anthony

Linear extrapolation would be more useful than linear interpolation when you need to predict values beyond the range of known data points. It is commonly used in scenarios where you want to forecast future trends or outcomes based on existing data. Extrapolation extends the linear relationship observed within a given range to make predictions outside that range, while interpolation estimates values within the known range based on existing data points. Therefore, if you need to make predictions about future trends or outcomes, linear extrapolation would be the appropriate choice.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.