The function = log10 is going to be approximated using an interpolation function for 1 ≤ ≤ 10. (a) How many data points for piecewise linear interpolation are needed to guarantee the error is less...

The function
= log₁₀

is going to be approximated using an interpolation function for 1 ≤

≤ 10.

(a) How many data points for piecewise linear interpolation are needed to guarantee the error is less than 10⁻⁶?

(b) How many data points for a clamped cubic spline are needed to guarantee the error is less than 10⁻⁶?

(c) How many data points are needed when using Chebyshev interpolation to guarantee the error is less than 10⁻⁶?