Q1 (999 points) Let r(t) = e² (1, sint, cost) and let a = In 2. (A) (20%) Calculate, to four significant figures, the straight-line distance S₁ from r(0) to r(a). (B) (20%) Calculate, to four significant figures, the sum S2 of the two straight-line distances from r(0) to r(a/2) and from r(a/2) to r(a). (C) (60%) As discussed in class, S1 and S2 are approximations to the arclength of r(t) from t = 0 tot = a. Calculate, for each of (A) and (B), the percent errors (the absolute value of the actual arc length minus the approximation, divided by the actual, times 100).

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