Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 28L / e / Solution

For ${\delta }_c=cX$, $R=c^2+(1-c{)}^2{\theta }^2$. Thus $I_{\gamma }=[-\sqrt{\gamma -c^2}/(1-c),\sqrt{\gamma -c^2}/(1-c)]$, with the stated length. Substitution (or elementary algebra) verifies it is at most the bound in part (d).

Solved by gpt-5.6-sol high.