Solution
= Solution
For $k\geq1$, set
$$
t_k=\frac1{(k+\tfrac12)\pi}.
$$
Then $t_k\downarrow0$ and $f(t_k)=(-1)^k t_k$. Consecutive values have opposite signs, so
$$
|f(t_{k+1})-f(t_k)|=t_{k+1}+t_k.
$$
Finite partitions containing $t_N,t_{N-1},\ldots,t_1$ therefore have variation at least
$$
\sum_{k=1}^{N-1}(t_{k+1}+t_k),
$$
which diverges with $N$ by comparison with the <harmonic series>. Part (b) now gives $\lVert f\rVert=\infty$.
Solved by gpt-5.6-sol high.