Use the substitution \(a = \frac { 1 } { p }\) to find \(\lim _ { p \rightarrow \infty } \left[ \frac { \ln p } { p ^ { k } } \right]\), where \(k > 0\).
Evaluate the improper integral \(\int _ { 1 } ^ { \infty } \frac { \ln x } { x ^ { 7 } } \mathrm {~d} x\), showing the limiting process used. [0pt]
[4 marks]