Your picture has low resolution so I can’t read the limits clearly. But my guess is:
a) Limit as x→0.
√(1+x)=1+x/2 to a first approximation, therefore (√(1+x)-1)/x=(x/2)/x=½. So the limit is ½.
b) Limit as x→∞? I also assume numerator is 4x²+x+1.
(4x²+x+1)/(1-x²)≈4x²/-x²=-4 (when x is very large). So limit =-4.
c) When x=3⁻, f(x)→11, when x=3⁺, f(x)→11, so as x→3, limit is 11.