Components of the dilepton continuum in Pb+Pb collisions at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msqrt><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:msqrt><mml:mo>=</mml:mo><mml:mn>2.76</mml:mn></mml:mrow></mml:math>TeV

The dilepton invariant mass spectrum measured in heavy-ion collisions includes contributions from important quark-gluon plasma (QGP) probes such as thermal radiation and the quarkonium ($J/\ensuremath{\psi}$, ${\ensuremath{\psi}}^{\ensuremath{'}}$, and $\ensuremath{\Upsilon}$) states. Dileptons coming from hard $q\overline{q}$ scattering, the Drell-Yan process, contribute in all mass regions. In heavy-ion colliders, such as the Large Hadron Collider (LHC), semileptonic decays of heavy flavor hadrons provide a substantial contribution to the dilepton continuum. Because the dilepton continuum can provide quantitative information on heavy quark yields and their medium modifications, it is important to identify which dilepton sources populate different parts of the continuum. In the present study, we calculate $c\overline{c}$ and $b\overline{b}$ production and determine their contributions to the dilepton continuum in Pb+Pb collisions at $\sqrt{{s}_{{}_{NN}}}=2.76$ TeV with and without including heavy quark energy loss. We also calculate the rates for Drell-Yan and thermal dilepton production. The contributions to the continuum from these dilepton sources are studied in the kinematic ranges relevant for the LHC detectors. The relatively high ${p}_{T}$ cutoff for single leptons excludes most dileptons produced by the thermal medium. Heavy flavors are the dominant source of dilepton production in all the kinematic regimes except at forward rapidities where Drell-Yan dileptons become dominant for masses greater than 10 GeV/${c}^{2}$.