Maths Limits?

Sol
A=lim(x->0+)_(1+2^(1/x)]/[3+2^(1/x)]
Set y=2^(1/x)
x->0+ => y->∞
A=lim(y->∞)_(1+y)/(3+y)=lmi(y->∞)_(1/y+1)/(3/y+1)=1
B=lim(x->0－)_(1+2^(1/x)]/[3+2^(1/x)]
Set z=2^(1/x)
x->0－ => z->0
B=lim(z->0)_(1+z)/(3+z)=1/3
A<>B
lim(x->0)_[1+2^(1/x)]/[3+2^(1/x)]不存在

lim(x->0)_[1+2^(1/x)]/[3+2^(1/x)]
=lim(x->0)_[(2^x)/(2^x)][1+2^(1/x)]/[3+2^(1/x)]
=lim(x->0)_[(2^x)+1]/[3(2^x)+1]
=[(2^0)+1]/[3(2^0)+1]
=2/(3+1)
=0.5