Ejercicios Semana 15
Nombre: Laura Valentina Pinto Rojas Grupo: 1.1
𝐸𝑛𝑐𝑜𝑛𝑡𝑟𝑎𝑟 𝑠𝑢𝑠 𝑑𝑒𝑟𝑖𝑣𝑎𝑑𝑎𝑠 𝑦 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑟 𝑎 = 0
𝑓(𝑥)=(1 − 𝑥)−2 𝑓(0)= 1
𝑓(𝑥)′=2
(1−𝑥)3 𝑓(0)′= 2
𝑓(𝑥)′′ =6
(1 − 𝑥)4 𝑓(0)′′ = 6
𝑓(𝑥)′′′ =24
(1−𝑥)5 𝑓(0)′′′ =24
𝑈𝑡𝑖𝑙𝑖𝑧𝑎𝑟 𝑙𝑎 𝑓𝑜𝑟𝑚𝑢𝑙𝑎 𝑔𝑒𝑛𝑒𝑟𝑎𝑙 =
𝑓(𝑥)= 𝑓(𝑎)+ 𝑓(𝑎)′(𝑥 − 𝑎)+𝑓(𝑎)′′
2! (𝑥 − 𝑎)2+𝑓(𝑎)′′′
3! (𝑥 − 𝑎)3
𝑓(𝑥)= 1 +2(𝑥 −𝑎)+6
2!(𝑥 −𝑎)2+24
3! (𝑥 − 𝑎)3
𝑓(𝑥)= 1 + 2(𝑥 − 0)+6
2(𝑥 − 0)2+24
6(𝑥 − 0)3
𝑓(𝑥)= 1 + 2𝑥 + 3𝑥2+4𝑥3
𝐸𝑠𝑐𝑟𝑖𝑏𝑖𝑟 𝑒𝑛 𝑓𝑜𝑟𝑚𝑎 𝑑𝑒 𝑠𝑢𝑚𝑎 =
𝑓(𝑥)= ∑(𝑛 + 1)𝑥𝑛
∞
𝑛=0
