Question

Help understanding the solution to question 2A-5.
http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/part-a-approximation-and-curve-sketching/problem-set-3/MIT18_01SC_pset2sol.pdf

Answer 1

I understand all of the steps leading to the ratio \[ (1+\frac{\epsilon}{60})^3 \]. However, I do not understand the next step entirely. They multiply the weight of someone 60in tall, by an approximation of the above ratio:\[(1+\frac{3\epsilon}{60})\] I don't understand how that approximation was derived. Although I do understand the alternate method using derivatives.

Answer 2

Hi!
My understanding is as follows: If you expand
\[(1 + \frac{ \epsilon }{ 60 })^3\]
you would end up with the following terms:
\[1 + \frac{ \epsilon^3 }{60^3} + 3\frac{ \epsilon }{ 60 }+3\frac{ \epsilon^2 }{ 60^2 }\]
As \epsilon is small, the square and cube terms are even smaller (and thus negligible) and you'd end up with the approximation.
Hope this helps! Now, if you ask me, I prefer the second method mentioned in the answer :-)

Answer 3

Yep, that makes sense! Thank you!