Question

What is the limit of ((1/sqrt(1+x))-1)/(x) as x approaches 0?

Answer 1

lim as s->0 of \[\frac{ (1/\sqrt{1+x} -1 }{ x }\]

Answer 2

multiply num and denum by \(\sqrt{x+1}\)\[\frac{\frac{1}{\sqrt{x+1}}-1}{x}\]\[\frac{1-\sqrt{x+1}}{x\sqrt{x+1}}\]use conjugate of \(1-\sqrt{x+1}\) \[\frac{1-\sqrt{x+1}}{x\sqrt{x+1}}\times\frac{1+\sqrt{x+1}}{1+\sqrt{x+1}}\]????