antinerd
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Homework Statement
OK, I'm doing this linear approximation problem:
Approximate \sqrt{4.1} - \sqrt{3.9}
Homework Equations
f(a + h) ~ f(a) + hf`(a)
The Attempt at a Solution
This is what I have done so far:
I approximated each square root separately...
4.1 = 4 + h
h = .1
f(x) = \sqrt{x}
f`(x) = 1/(2\sqrt{x}
then I got:
\sqrt{x+h} ~ \sqrt{x} + h/(2\sqrt{x})
so that the approximation of \sqrt{4.1} is 2 + (.1/4)
I did the same thing for \sqrt{3.9} and got
2 - (.1/4)
Then I just took them and subtracted
2 + (.1/4) - 2 + (.1/4)
and got .2/4 as the approximation. It seems like it's erroneous. Could someone help me out with setting up this problem if I did it wrong?