Question

Lim√x+1 -2 /x-3 x-->3+

Answer 1

Lim  [ √(x+1) -2]/(x-3)
x-->3⁺

Lim  [ √(x+1) -2][ √(x+1) + 2]/(x-3)[ √(x+1) +2]
x-->3⁺

Lim  [ √(x+1)² -2²]/(x-3)[ √(x+1) +2]
x-->3⁺

Lim  [ x+1 - 4]/(x-3)[ √(x+1) +2]
x-->3⁺

Lim  [ x-3]/(x-3)[ √(x+1) +2]
x-->3⁺


Lim 1/[ √(x+1) +2]  =1/(2+2)=1/4
x-->3⁺