The correct option is C exists and equals 14√2
limy → 0 √1+√1+y4 − √2y4
Now rationalizing the numerator, we get
limy → 0 1 + √1+y4 − 2y4×1√1 + √1+y4 + √2
=limy → 0 1 + √1+y4 − 2y4×12√2
=limy → 0 √1+y4 − 1y4×12√2
=12√2×limy → 0 4y32√1+y44y3
[Using L Hopital rule]
=12√2×12=14√2