Q.A galvanic cell is built by combining a silver electrode dipped in $1\ \text{M}\ \text{AgNO}_3$ with a copper electrode dipped in $1\ \text{M}\ \text{CuSO}_4$. Using the standard reduction potentials $E^{\circ}(\text{Ag}^{+}/\text{Ag}) = +0.80\ \text{V}$ and $E^{\circ}(\text{Cu}^{2+}/\text{Cu}) = +0.34\ \text{V}$, identify the cathode, the anode, the oxidizing agent, and the reducing agent.

[!TLDR] $\text{Ag}^+/\text{Ag}$ has the higher (more positive) standard reduction potential, so silver is reduced (cathode) and copper is oxidized (anode). [!ANSWER] Cathode = silver electrode (reduction of $\text{Ag}^+$); anode = copper electrode (oxidation of $\text{Cu}$); oxidizing agent = $\text{Ag}^+$; reducing agent = $\text{Cu}$.

In any galvanic cell, the electrode with the higher (more positive) standard reduction potential is reduced and therefore acts as the cathode, while the electrode with the lower standard reduction potential is oxidized and acts as the anode. Here $E^{\circ}(\text{Ag}^{+}/\text{Ag}) = +0.80\ \text{V}$ is more positive than $E^{\circ}(\text{Cu}^{2+}/\text{Cu}) = +0.34\ \text{V}$, so silver ions are preferentially reduced: $2\text{Ag}^{+}(aq) + 2e^{-} \to 2\text{Ag}(s)$ at the cathode, and copper metal is oxidized: $\text{Cu}(s) \to \text{Cu}^{2+}(aq) + 2e^{-}$ at the anode. The overall spontaneous cell reaction is $\text{Cu}(s) + 2\text{Ag}^{+}(aq) \to \text{Cu}^{2+}(aq) + 2\text{Ag}(s)$. The species that is reduced ($\text{Ag}^+$) is, by definition, the oxidizing agent (it causes copper to be oxidized), and the species that is oxidized ($\text{Cu}$) is the reducing agent. [!ANSWER] Cathode = silver electrode; anode = copper electrode; oxidizing agent = $\text{Ag}^+$; reducing agent = $\text{Cu}$.

Compare the two standard reduction potentials directly: the higher one is reduced (cathode/oxidizing agent), the lower one is oxidized (anode/reducing agent).

Swapping the definitions of oxidizing and reducing agent — the oxidizing agent is the species that itself gets reduced, not the one that gets oxidized.