Sleep is an indication of a limited effect on the intervention of vampiric or parasitic nature. This value is true if the limb had a dream separate from the body. In any case, the image is an indication of the effect, which has as consequence that deviates from the subject's own integrity. If you dreamed of limb together with the body, the dream may reflect the influence of the parasitic.
To see a tree limb in your dream, symbolizes the relationships and communication between you and your family or relatives. Alternatively, the limb represents your developing abilities and budding talents. The dream may also be a metaphor that you are "going on out on a limb". The odds are against you.
If the limb refers to a body part, then look at the significance of the specific limb.