Counter-Example for Riesz representation Theorem The following is an exercise of Conway's Functional analysis, chapter 1, section 3.
Let $H=L^2(0,1)$ and $C^{(1)}$ be the set of all continuous functions on $[0,1]$ that have a continuous derivative. Let $t\in [0,1]$ and define $L:C^{(1)}\longrightarrow \mathbb{F}$ by $L(h)=h'(t)$. Show that there is no bounded linear functional on $H$ that agrees with $L$ on $C^{(1)}$.

Hint: Let $h_n(t)=\sin nt$. What is the $L^2$ norm of $h_n$? And of $h_n'$?
