Taking ln 5=1.61, use differentials to estimate ln 5.2?

Question

Taking ln 5=1.61, use differentials to estimate ln 5.2?

Answer 1

Take the Taylor series at x= 5 for ln x

f(x) = f(5) +(x-5) f´(5) +(x-5)^2/2 f´´(5)

I think you are asked to take the two first terms

ln(5.2)=1.61+0.2*1/5 = 1.61+0.04 = 1.65