Limites tendendo a infinito Gabarito

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CENTRO UNIVERSITÁRIO CARIOCA CÁLCULO I 
 
Catiúscia A. B. Borges 1 
 
Lista 03- Limite tendendo a infinito 
 
1) Observe os gráficos abaixo e determine cada limite: 
 
a) 
 
lim𝑥→−∞ 𝑓(𝑥) = −∞ 
 
 
lim𝑥→+∞ 𝑓(𝑥) = +∞ 
 
 
 
 
b) 
 
lim𝑥→−∞ 𝑓(𝑥) = +∞ 
 
 
lim𝑥→+∞ 𝑓(𝑥) = −∞ 
 
 
 
c) 
 
lim𝑥→−∞ 𝑓(𝑥) = +∞ 
 
 
lim𝑥→+∞ 𝑓(𝑥) = +∞ 
 
 
 
d) 
 
 
lim𝑥→−∞ 𝑓(𝑥) = −∞ 
 
 
lim𝑥→+∞ 𝑓(𝑥) = +∞ 
 
 
 
 
 
 
 
CENTRO UNIVERSITÁRIO CARIOCA CÁLCULO I 
 
Catiúscia A. B. Borges 2 
 
e) 
 
lim𝑥→−∞ 𝑓(𝑥) = 3 
 
 
lim𝑥→+∞ 𝑓(𝑥) = 3 
 
 
 
f) 
 
lim𝑥→−∞ 𝑓(𝑥) = 0 
 
 
lim𝑥→+∞ 𝑓(𝑥) = +∞ 
 
 
 
 
g) 
 
 
lim𝑥→−∞ 𝑓(𝑥) = +∞ 
 
 
lim𝑥→+∞ 𝑓(𝑥) = 0 
 
 
2) Determine cada limite: 
 
a) lim𝑥→+∞ 4𝑥
3 − 3𝑥2 + 𝑥 − 10 = +∞ 
 
 
b) lim𝑥→−∞ 4𝑥
3 − 3𝑥2 + 𝑥 − 10 = −∞ 
 
 
c) lim𝑥→+∞−6𝑥
4 + 4𝑥3 − 3𝑥² + 𝑥 − 10 = −∞ 
 
 
d) lim𝑥→−∞−6𝑥
4 + 4𝑥3 − 3𝑥2 + 𝑥 − 10 = −∞ 
 
 
e) lim𝑥→+∞
4𝑥3−3𝑥2+𝑥−10
3𝑥2+𝑥+8
= lim𝑥→+∞
4𝑥3
3𝑥2
= lim𝑥→+∞
4
3
𝑥 = +∞ 
3 
 
 
CENTRO UNIVERSITÁRIO CARIOCA CÁLCULO I 
 
Catiúscia A. B. Borges 3 
 
 
f) lim𝑥→−∞
𝑥7+4𝑥5+𝑥
𝑥³−3𝑥2+19
= lim𝑥→−∞
𝑥7
𝑥³
= lim𝑥→−∞ 𝑥
4 = +∞ 
 
 
 
g) lim𝑥→−∞
−8𝑥5+4𝑥3+𝑥
𝑥³−3𝑥2+19
= lim𝑥→−∞
−8𝑥5
𝑥³
= lim𝑥→−∞−8𝑥
2 = −∞ 
 
 
h) lim𝑥→+∞
−4𝑥3−3𝑥2+𝑥−10
3𝑥2+𝑥+8
= lim𝑥→+∞
−4𝑥3
3𝑥2
= lim𝑥→+∞
−4
3
𝑥 = −∞ 
 
 
i) lim𝑥→−∞
𝑥³−3𝑥2+19
−8𝑥5+4𝑥3+𝑥
= lim𝑥→−∞
𝑥³
−8𝑥5
= lim𝑥→−∞
−1
8𝑥2
= 0 
 
 
j) lim𝑥→+∞
43𝑥2+𝑥+8
𝑥3−3𝑥2+𝑥−10
= lim𝑥→+∞
43𝑥2
𝑥3
= lim𝑥→+∞
43
𝑥
=0 
 
 
k) lim𝑥→−∞
𝑥³−3𝑥2+19
𝑥7+4𝑥5+𝑥
= lim𝑥→−∞
𝑥³
𝑥7
= lim𝑥→−∞
1
𝑥4
= 0 
 
 
l) lim𝑥→+∞
3𝑥2+𝑥+8
−4𝑥3−3𝑥2+𝑥−10
= lim𝑥→+∞
3𝑥2
−4𝑥3
= lim𝑥→+∞
−3
4𝑥
= 0 
 
 
m) lim𝑥→−∞
20𝑥7−3𝑥2+19
4𝑥7+4𝑥5+𝑥
= lim𝑥→−∞
20𝑥7
4𝑥7
=
20
4
= 5 
 
 
n) lim𝑥→+∞
3𝑥³+𝑥+8
−4𝑥3−3𝑥2+𝑥−10
= lim𝑥→+∞
3𝑥³
−4𝑥3
= −
3
4