SOLUTION: state the linear approximation of √99.95

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Question 1036453: state the linear approximation of √99.95
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
state the linear approximation of √99.95
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L(x) = f(a) + f'(a)(x-a)
a = 100
f(x) = x^(1/2)
f'(x) = 1/(2*sqrt(x))
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L(sqrt(99.95)) = 10 + f'(100)(100-99.95)
L(sqrt(99.95)) = 10 + 1/(2*10)*(-0.05)
L(sqrt(99.95)) = 10 - 0.0025
L(sqrt(99.95)) = 9.9975
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Cheers,
Stan H.

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
state the linear approximation of sqrt(99.95)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

sqrt%2899.95%29 = sqrt%28100+-+0.05%29 = sqrt%28100%2A%281-0.05%2F100%29%29 = 10%2Asqrt%281+-+0.0005%29 = 10%2A%281+-+0.0005%2F2%29 = 10*(1-0.00025) = 10*0.99975 = 9.9975.


The key moment is this approximation

sqrt%281+-+x%29 = 1+-+x%2F2 (approximately) which is valid for small values of x  (small comparatively with the value of 1).