Find the linear approximation of f(x)=ln x at x=1

Question

where L(x)=

Answer 1

y = ln x
m = dy/dx = 1/x
at x = 1, m = 1/1 = 1
so
y = x + b
at x = 1, y = ln 1 = 0
so
0 = 1*1 + b
so
b = -1
so
y = x - 1