Provide an appropriate response.(a) Show that dx = e-4 < 0.0092 and hence that dx < 0.0092.(b) Explain why this means that dx can be replaced by dx without introducing an error of magnitude greater than 0.0092.

Question

What will be an ideal response?

Answer 1

(a) dx = dx =  - e^-2b + e^-4 = e^-4 < 0.0092
(b) Since 0 < e^-x2 ? e^-2x for x ? 2, dx ? dx . So dx < 0.0092. Therefore,  dx = dx + dx ? dx, with an error of magnitude no greater than 0.0092.