(a) is continuous at if
So you want both limits to equal , which is .
For the left limit, we use . The limit as is , so needs to be . Now, since the other equation for also depends on , we have to hope that works for it as well. And it does: , so implies is continuous at .
(b) Here you want (and also ).
(c) Here you want the function to blow up near , so what value of can you choose so that or as ?
(d) Here you want . This is basically a "what's left over" question. Any value of that was not an answer to one of the above parts will work here.