Find the exact limit of ...

find the exact limit of [ sqrt(3+x) - sqrt(3) ] / x

as x approaches 0


use the limit Laws to find the exact value

Using conjugates:
lim(x→0) (√(3+x) - √3) / x
= lim(x→0) (√(3+x) - √3) * (√(3+x) + √x) / [x * (√(3+x) + √3)]
= lim(x→0) ((3+x) - 3) / [x(√(3+x) + √3)]
= lim(x→0) x / [x(√(3+x) + √3)]
= lim(x→0) 1 / (√(3+x) + √3)
= 1/(2√3).

I hope this helps!