In Acts 9:36-43, we read again how the power that Jesus had has been imparted to the disciples. In Acts we've already read about the lame and sick and demon-possessed being healed by the disciples. They're doing amazing things. But in this story we read about Peter raising Tabitha from the dead. 

This passage is very similar to the one about Jesus raising Jairus' daughter in Luke 8:40–56. In that encounter, Jesus allows only a few to accompany him into the room where the dead girl lay. He takes her by the hand, speaks to her, tells her to arise, and she gets up at once. The parallels with Tabitha's awakening from death are clear and intentional. This story is as much about saying that Peter and the apostles have the same power as Jesus as it is about the healing itself. And that's why it's so unbelievable.

I don't have a problem believing that Peter could raise the dead. That's remarkable, yes, but I don't doubt that part of the story. The part that I have trouble with is the fact that, in response to Peter's resuscitation of Tabitha, the people believe in Jesus—not Peter.