Linear Approximation

Linear Approximation

Here I will attempt to use linear approximation to estimate the value of ln(1.07)

The first thing you need to do when performing a linear approximation is set up an equation with known numbers as variables:

y = f(x) = ln(x) here we have turned 1.07 into “x”.

Now take the derivative of either side; dy = \frac{1}{x} dx when x = 1 and dx = 0.07

dy = \frac{1}{1} (0.07) = 0.07

ln(1.07) = f(1.07) because our f(x) function was equal to ln(x), so we know in this case, that x = 1.07, after all, it was given in the problem.

f(1.07) \approx f(1) + dy = 0 + 0.07 = 0.07.

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