7. Given the graph of a differentiable function f(x), we would like to calculate the length of the curve in the graph. (For example the length of the curve in the figure to Problem 1.) (a) If you had a piece of string and a ruler, how could you determine the length of the curve? (b) Suppose you only had a ruler, how could we determine the length? Is this precise or an approxi- mation? (c) Suppose we only have the coordinate axes, not a ruler and no string. How could we then approx- imate the length? This should involve the Pythagorean Theorem, a sum and differentials. (d) How could we improve the accuracy of our estimate? What would be the most precise answer?

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