Question

qual o lim(x+10)/ln(x ao quadrado +1) quando x tende a 0?

Answer 1

Resposta:

lim(x->0) (x + 10)/ln(x^2 + 1) = +∞

Explicação passo-a-passo:

Find the following limit:

lim(x->0) (x + 10)/ln(x^2 + 1)

Applying the product rule, write

lim (x->0) (x + 10)/ln(x^2 + 1) as

lim (x->0)(x + 10) × (lim(x->0) 1/ln(x^2 + 1)):

lim (x->0)(x + 10) = 0 + 10 = 10:

10×lim (x->0) 1/ln(x^2 + 1)

Since lim (x->0) ln(x^2 + 1) = 0 and

ln(x^2 + 1)>0 for all x near x = 0,

lim_(x->0) 1/ln(x^2 + 1) = +∞

10×(+∞) = +∞

Answer: +∞