Find the linear approximation L(x) of

Question

ln(x)at the point a = 12.

Answer 1

L(x)=ln(z)+delta(x-z)*dL/dx

L(x)=ln(12)+1/12*(x-12)
so for example, what is Ln(13):
Ans: Ln(13)=ln(12)+1/12*1

checking that from a calculator:
ln(12)== 2.48490665
ln(13)== 2.56494936
difference 0.08004271
1/12== 0.0833333333