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Verify the given linear approximation at a = 0.Then determine the values of x for which the linear approximation is accurate to...Question
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) ā x
xE
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) ā x
xE
Answers
Damon
Linear approximation to what function?
Did you try to copy and paste? If so, that does not work here.
Did you try to copy and paste? If so, that does not work here.
Tim
The question was like this!
Damon
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