Show that the cosine integral \(\mathrm { C i } x \equiv - \int _ { x } ^ { \infty } \frac { \cos t } { t } d t\) for large enough x can be approximated as \(\mathrm { C i } x \approx { \frac { \sin x } { x } }\) . Find the region of x for which the relative error of this approximation is less than \(1 0 ^ { - 4 }\)
Asymptotic approximation of the cosine integral $\operatorname{Ci}x$
P-TRIV-RA30
- Area
- Real Analysis
- Status
- draft