Ejercicio de calculo
- 2. a) lim
𝑥→0−
𝑓 𝑥
b) lim
𝑥→0+
𝑥)
c) lim
𝑥→0
𝑓(𝑥)
𝑓 𝑥 =
𝑥2
+ 𝑥
𝑥3 + 𝑥2
a) lim
𝑥→0−
= lim
𝑥→0−
𝑥(𝑥 + 1)
𝑥2(𝑥 + 1)
= lim
𝑥→0−
𝑥(𝑥 + 1)
𝑥 𝑥 + 1
= lim
𝑥→0−
𝑥(𝑥 + 1)
−𝑥 𝑥 + 1
= lim
𝑥→0−
𝑥 + 1
− 𝑥 + 1
∙
𝑥 + 1
𝑥 + 1
lim
𝑥→0−
𝑥 + 1 𝑥 + 1
− 𝑥 + 1
=
𝑥 + 1
−1
= lim
𝑥→0−
− 𝑥 + 1 = − 0 + 1 = −1
b) lim
𝑥→0+
𝑥2 + 𝑥
𝑥3 + 𝑥2
= lim
𝑥→0+
𝑥(𝑥 + 1)
𝑥2(𝑥 + 1)
= lim
𝑥→0+
𝑥(𝑥 + 1)
𝑥 𝑥 + 1
= lim
𝑥→0+
𝑥 + 1
𝑥 𝑥 + 1
= lim
𝑥→0+
𝑥 + 1
𝑥 + 1
∙
𝑥 + 1
𝑥 + 1
lim
𝑥→0+
(𝑥 + 1)( 𝑥 + 1)
(𝑥 + 1)
= lim
𝑥→0+
𝑥 + 1
1
= lim
𝑥→0+
𝑥 + 1 = 0 + 1 = 1
𝑐) lim
𝑥→0
𝑓(𝑥) = ∄ ∴ 𝑒𝑙 𝑙í𝑚𝑖𝑡𝑒 𝑑𝑒 𝑙𝑎 𝑓𝑢𝑛𝑐𝑖ó𝑛 𝑛𝑜 𝑒𝑥𝑖𝑠𝑡𝑒, 𝑝𝑜𝑟𝑞𝑢𝑒 𝑙𝑜𝑠 𝑙í𝑚𝑖𝑡𝑒𝑠 𝑙𝑎𝑡𝑒𝑟𝑎𝑙𝑒𝑠 𝑡𝑖𝑒𝑛𝑒𝑛 𝑑𝑖𝑟𝑒𝑓𝑒𝑛𝑡𝑒𝑠 𝑣𝑎𝑙𝑜𝑟𝑒𝑠.