Lim [tex] frac{ x^{2} }{1- sqrt{1

+ x^{2} } } [/tex]
X⇔0

Tolong klikan sekawan bkan di subsitusikan

Lim [tex] frac{ x^{2} }{1- sqrt{1

Jawaban Terkonfirmasi

Dengan metode perkalian sekawan:
$$begin{align}lim_{xto0}frac{x^2}{1-sqrt{1+x^2}}&=lim_{xto0}frac{x^2}{1-sqrt{1+x^2}}timesfrac{1+sqrt{1+x^2}}{1+sqrt{1+x^2}} \ &=lim_{xto0}frac{x^2(1+sqrt{1+x^2})}{1^2-sqrt{(1+x^2)^2}} \ &=lim_{xto0}frac{x^2(1+sqrt{1+x^2})}{1-(1+x^2)} \ &=lim_{xto0}frac{x^2(1+sqrt{1+x^2})}{1-1-x^2} \ &=lim_{xto0}frac{x^2(1+sqrt{1+x^2})}{-x^2} \ &=lim_{xto0}-(1+sqrt{1+x^2}) \ &=-(1+sqrt{1+0^2}) \ &=-(1+sqrt{1}) \ &=-(1+1) \ &=-2 end{align}$