Question

Qual o limite de $\lim_{x \to \ 4} \frac{4 - x}{ 5 - \sqrt{x^{2} + 9 } }$

Answer 1

Resposta:

lim   (4-x)/[5-√(x²+9)]

x-->4

lim   (4-x)[5+√(x²+9)] /[5-√(x²+9)][5+√(x²+9)]

x-->4

lim   (4-x)[5+√(x²+9)] /[5²-√(x²+9)²]

x-->4

lim   (4-x)[5+√(x²+9)] /[25-9-x²]

x-->4

lim   (4-x)[5+√(x²+9)] /[16-x²]

x-->4

lim   (4-x)[5+√(x²+9)] /[(4-x)*(4+x)]

x-->4

lim   [5+√(x²+9)] /(4+x) =(5+5)/8 = 5/4

x-->4