Solutions - 0140-05

(a) $5/12$ $$ (b) diverges $$ (c) $2$

(d) $0$

Observe that $\frac{n^3}{n^3+1}\to 1$ as $n\to \infty$, but for each $n$, the value is below $1$, in the domain of ${\cos }^{-1}(x)$, which is continuous for $x\in (-1,+1)$.

(e) $10$