Question

Approximate the value of ln(1.1) using the tangent to f(x)=lnx at point x=1?

Answer 1

The value of `ln(1.1)` is approximately `0.1`.

Explanation:

We know that `f(1) = ln(1) = 0`. Furthermore, we know that `f'(x) = 1/x`. This means that `f'(1) = 1`.

The equation of the tangent line is given by

`y -y_1 = m(x - x_1)`

`y - 0 = 1(x -1)`

`y = x - 1`

When `x = 1.1` this means that `y = 1.1 - 1 ~~ 0.1`

The actual value of `ln(1.1)` is `0.095` so the estimation is quite good.

Hopefully this helps!