Sorry to be a hassle but i really don't see how this is fundamentally going to answer the question which is proving that the limit equals (∣f″(x∗)∣/2∣f′(x∗)∣))^q−1.
To get the top right to look like the top left you raise it to the power 1/β
To get the bottom right to look like the bottom left you raise to the power β+1
Im failing to see how this helps to answer the question though.