Question

f(x)
first two termo in expansion of log (1+e^x)
by Macheurin's theorem is​

Answer 1

Answer:

THIS IS A WRONG ANSWER SO DON"T WRITE IT AND THINK THAT ITS CORRECT

(MEME)

Step-by-step explanation:

A standard way to obtain the Taylor series about 0 is

∑k=0∞f(k)(0)k!⋅xk

Since f(x)=log(1+ex), we have

f(0)=log(1+e0)=log(2)

f′(0)=ex1+ex∣∣∣x=0=12

f′′(0)=ex(1+ex)2∣∣∣x=0=14

f′′′(0)=ex(1−ex)(1+ex)3∣∣∣x=0=0

Hence, we have the Taylor series about 0 to be

log(2)+x2+x28+O(x4)