Given fx In x use the tangent line approximation to find In

Given f(x) = In x, use the tangent line approximation to find In (1.1) Select one 0.0953 0.1 0.0032 1.05

Solution

The equation of the line tangent to a function f(x) at a point a is given by

f(x) = f(a) + ( x - a )f\'(a) --------------- (1)

Let f(x) = ln(x) then f\'(x) = 1/x

plug in f(x) = ln(x) , a = 1 and x = 1.1, in (1) we get

ln(1.1) = ln(1) + (1.1-1)(1/1)

= 0 + 0.1

= 0.1

Therefore , ln(1.1) = 0.1