# When $0\le h \le 0.01$, show that $e^h$ may be replaced by $1+h$ with an error of magnitude no greater than $0.6$% of h.

When $0\le h \le 0.01$, show that $e^h$ may be replaced by $1+h$ with an error of magnitude no greater than $0.6$% of h.

use $e^{0.001} = 1.01$

What I did was :-

• The error is not bounded by the next term; this is an error. This technique is only valid for alternating series. Instead use Taylor's theorem. – vadim123 Dec 7 '15 at 18:41
• Use Taylor expansion upper bounded by geometric series to get: $\frac {e^h-1-h}{h}\le \frac h {2(1-h)}$. – A.S. Dec 7 '15 at 19:04
• How to do this? – dknight Dec 8 '15 at 4:59