Linear approximation to what function?
Did you try to copy and paste? If so, that does not work here.
Verify the given linear approximation at
a = 0.
Then determine the values of x for which the linear approximation is accurate to within 0.1. (Enter your answer using interval notation. Round your answers to three decimal places.)
ln(1 + x) ≈ x
xE
3 answers
The question was like this!
Oh, I see
f(x) = ln (1+x)
df/dx = 1/(1+x)
d^2f/dx^2 = -1/(1+x)^2
f(x) = f(0) + [1/(1+0)] x - x^2/2! ...
f(x) = 0 + x - x^2/2 + .....
well at a first cut when is x^2/2 =.1 x?
x/2 = .1
x = .2
f(x) = ln (1+x)
df/dx = 1/(1+x)
d^2f/dx^2 = -1/(1+x)^2
f(x) = f(0) + [1/(1+0)] x - x^2/2! ...
f(x) = 0 + x - x^2/2 + .....
well at a first cut when is x^2/2 =.1 x?
x/2 = .1
x = .2