How do you find the linear approximation of (1.999)^4(1.999)4 ?
1 Answer
You can use the tangent line approximation to create a linear function that gives a really close answer.
Let's put
The linear approximation we want (see my other answer) is
f(x) ~~ f(a) + f'(a)(x-a)
f(1.999) ~~ f(2) + f'(2)(1.999-2)
~~ 2^4 + 4*2^3*(-0.001) = 16 - 0.032 = 15.968
You can compare to the actual exact result of
Bonus insight: The error depends on higher derivatives and can be predicted in advance! \ dansmath strikes again, approximately! /
