Question: Tabulate the function f(x) = x 3 for x = 4.8(0.1)5.6. Construct a table equivalent to Figure 2.102, and hence estimate the largest error that

Tabulate the function f(x) = x³ for x = 4.8(0.1)5.6. Construct a table equivalent to Figure 2.102, and hence estimate the largest error that would be incurred in using linear interpolation in your table of values over the range [5.0, 5.4]. Construct a similar table for x = 4.8(0.2)5.6 (that is, for linear interpolation with twice the tabulation interval) and estimate the largest error that would be incurred by linear interpolation from this table in the range [5.0, 5.4]. What do you think the maximum error in interpolating in a similar table formed for x = 4.8(0.05)5.6 might be? What tabulation interval do you think would be needed to allow linear interpolation accurate to 3dp?

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