If Nessie really loves Jacob then she might even sucide. または might go into deppesion like Bella did when Edward left. If the eqution really is {Renesmee + Jacob = 愛 for them }then she will NOT be able to live without him.
I don't think he will die because there is no reason for him to give up changing into a werewolf. The Only way he can age is によって stopping changing and since Renesmee will live forever, he will choose to stay werewolf and not age with her.
I think Nessie will react like her mother but in a controlled way like her father. Sure, for the first few days she'd be awfully sad but she'll manage to 移動する on but will still 愛 Jake because she's part vamp, means things are permanent for her.
But I think Jake can live forever, all he has to do is not to stop phasing. he just has to keep on being a wolf, which is possible since he within vampire vicinity