Solution
= 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).
= 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).