Question

lim n-->infinito (x+1)^2/x^2+1

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Answer 1

Resposta:

lim  (x+1)²/(x²+1)

x-->∞

lim  (x²+2x+1)/(x²+1)

x-->∞

lim        x²/(x²+1)  +2x/(x²+1) + 1/(x²+1)

x-->∞

lim        1/(1+1/x²)  +1/(x/2+1)/(x²+1) + 1/(x²+1)

x-->∞

= 1/(1+1/∞)  +1/(∞/2+1) + 1/(∞+1)

=      1/(1+0)  +1/(∞)+ 1/(∞+1)

=1+0+0  = 1   é a resposta

Observe:

1/∞ =0

∞/2 + 1  = ∞

∞²= ∞