(1)
lim(x->1) (x-1)/(√x-1)=lim(x->1) (√x-1)(√x+1)/(√x-1)=lim(x->1) (√x+1) =2
(2)
lim(x->+∞) x[√(x^2+1) -x ]
=lim(x->+∞) x[(x^2+1) -x^2]/[√(x^2+1) +x ]
=lim(x->+∞) x/[√(x^2+1) +x ]
=lim(x->+∞) 1/[√(1+1/x^2) +1 ]
=1/2
(3)
lim(x->0) x.sin(1/x) =0
(4)
lim(x->0) sinx.cos(1/x) =0
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