Question

Calcule o limite:
(√(X²+100)-100)/X²

Answer 1

lim    [raiz(x² + 100) - 100] / x²
x->0

L'Hôspital e Rega da Cadeia

lim      [1/2(x² + 100)^(-1/2) * 2x] / 2x
x->0

lim      $\frac{1}{ 2\sqrt{x^2 + 100} }$
x->0

= $\frac{1}{2 \sqrt{0+100} }$

= $\frac{1}{2.10} = \frac{1}{20}$