Question

Resolva os limites:

Answer 1

b) lim 9x^2-1/3x-1 x tende a 1/3
... lim (3x-1)(3x+1)/3x-1 quando x tende a 1/3
lim 3x+1 quando x tende a 1/3 >> 3(1/3) +1 = 2
e) lim x^3+8/x+2 quando x tende a -2
lim (x+2)(x^2-2x+4)/(x+2) quando x tende a -2>>
lim x^2-2x+4 quando x tende a -2  >>> (-2)^2-2(-2)+4 = 4+4+4 = 12

Answer 2

$\lim_{x \to \frac{1}{3} } \frac{9x^{2}-1 }{3x-1}= \lim_{x \to \frac{1}{3} } \frac{(3x-1)(3x+1) }{3x-1} =\\\\=\lim_{x \to \frac{1}{3} } 3x+1 = 3(\frac{1}{3} )+1=2$

$\lim_{x \to-2} \frac{x^{3}+8 }{x+2} =\lim_{x \to-2 } \frac{(x+2)(x^{2}-2x+4 ) }{x+2} =\\\\\lim_{x \to -2 } (x^{2}-2x+4 ) =(-2)^{2} -2(-2)+4=4+4+4=12$