- (i) (a) Explain why \(\int _ { 0 } ^ { \infty } \cosh x \mathrm {~d} x\) is an improper integral.
(b) Show that \(\int _ { 0 } ^ { \infty } \cosh x \mathrm {~d} x\) is divergent.
(ii)
$$4 \sinh x = p \cosh x \quad \text { where } p \text { is a real constant }$$
Given that this equation has real solutions, determine the range of possible values for \(p\)