MATH-2413-024
Henry Francis
Homework: Sec. 5.1
Question 7, 5.1.15
Part 1 of 2
HW Score: \( 94.12 \%, 16 \) of 17 points
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The velocity of an object moving along a line is given by \( \mathrm{v}=2 \mathrm{t}^{2}+4 \mathrm{ft} / \mathrm{s} \) on the interval \( 1 \leq \mathrm{t} \leq 5 \).
a. Divide the interval \( [1,5] \) into subintervals, \( [1,2],[2,3],[3,4] \), and \( [4,5] \). On each subinterval, assume the object moves at a constant velocity equal to the value of \( \mathrm{v} \) evaluated at the midpoint of the subinterval and use these approximations to estimate the displacement of the object on \( [1,5] \). (See part (a) of the figure.)
b. Repeat part (a) for \( \mathrm{n}=8 \) subintervals (see part (b) of the figure).
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a. For \( \mathrm{n}=4 \) subintervals, the approximate displacement of the object is \( \square \) \( \mathrm{ft} \)