Science:Math Exam Resources/Courses/MATH110/April 2018/Question 08 (c)/Solution 1

Answer for MATH 110:

The accuracy of the linear approximation depends on the distance between the point ${\textstyle x=a}$ and the ${\textstyle x}$-value of the point we are trying to estimate: in general a function only behaves approximately like a linear function between two points that are very close together. This would suggest that the first approximation should be more accurate, since the ${\textstyle x}$-values only differ by ${\textstyle 0.5}$ whereas in the second approximation they differ by ${\textstyle e-1}$ which is more than three times as big.

Answer: One would expect the linear approximation from ${\textstyle {\color {blue}(a)}}$ to be more accurate.