Lim (√(3-x) - √(3+x)) /x
x->0
2 answers
-1/sqrt(3)
I think you wanted to know how:
multily numerator and denom by
sqrt(3-x) + sqrt(3+x)
lim ( 3-x -3-x) )/(x(sqrt(3-x) + sqrt(3+x))
lim(-2x/x(sqrt(3-x) + sqrt(3+x)))
lim -2/(sqrt(3-x) + sqrt(3+x))
=-1/sqrt(3)
multily numerator and denom by
sqrt(3-x) + sqrt(3+x)
lim ( 3-x -3-x) )/(x(sqrt(3-x) + sqrt(3+x))
lim(-2x/x(sqrt(3-x) + sqrt(3+x)))
lim -2/(sqrt(3-x) + sqrt(3+x))
=-1/sqrt(3)