Question

O limite de x tendendo a 0 (raiz de x²+x+1)-1 dividido por x

Answer 1

Boa dia.

lim (√(x² + x + 1)-1)/x

d/dx(√(x² + x + 1) - 1) = (2x + 1)/(2√(x² + x + 1))
d/dx (x) = 1

lim (√(x² + x + 1)-1)/x = (2x + 1)/(2√(x² + x + 1)) = 1/2 
x-->0                              x-->0