= Solution
The comoving distance to the <Cosmic microwave background last-scattering surface> is of order the present horizon, $\chi_*\sim1.3\times10^4\,\mathrm{Mpc}$. At recombination the particle horizon is much smaller, so replacing $\chi_*$ by today's horizon is adequate for the requested estimate. A transverse <Fourier mode> projects approximately to angular multipole $\ell\sim k\chi_*$. If an angular feature's width is estimated by $\theta\sim1/\ell$, the resolution $\theta_{\min}\sim10^{-3}$ gives
$$
k_{\max}\sim\frac1{\chi_*\theta_{\min}}\sim0.08\,\mathrm{Mpc^{-1}}.
$$
Using the common half-wavelength convention $\theta\sim\pi/\ell$ instead gives $\ell_{\max}\sim3000$ and $k_{\max}\sim0.2$--$0.3\,\mathrm{Mpc^{-1}}$. These express the same order-of-magnitude resolution estimate with different angular-scale conventions. On the graph, a useful indicative band is therefore \b[from about $10^{-4}\,\mathrm{Mpc^{-1}}$ to order $10^{-1}\,\mathrm{Mpc^{-1}}$, potentially a few times $10^{-1}$]; it is not a sharp instrumental boundary. The lowest useful multipoles are of order a few, with substantial <cosmic variance>.
The <cosmic microwave background> constrains the <matter power spectrum> indirectly through the primordial spectrum and radiation/matter <cosmological transfer functions>. Beam resolution, <Cosmic microwave background diffusion damping>, foreground emission, and projection of three-dimensional fluctuations into angular anisotropy limit the recoverable small-scale information. Resolving a given angle alone does not guarantee a precise matter-spectrum measurement there.
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