Find the linear approximation of the function f(x) = √1-x at a = 0 and use it to approximate the numbers √0.9?

Find the linear approximation of the function f(x) = √1-x at a = 0 and use it to approximate the numbers √0.9 and √0.99. (Round your answers to four decimal places.)

Answer 1

You should get…

L(x) = f'(a)(x – a) + f(a)
= -½ * x + 1
= -x/2 + 1

Now…

L(0.1) = 0.95
L(0.01) = 0.995

Good luck!

Source(s): ☻

Answer 2

L(x) = f(a) + f ‘ (a) * (x – a) (linearization formula) f(x) = sqrt(a million-x) f(0) = a million f ‘ (x) = (a million/2) * (a million-x)^(-a million/2) f ‘ (0) = (a million/2) * (a million)^(-a million/2) f ‘ (0) = a million/2 L(x) = a million + (a million/2) * (x – a million/2) L(x) = a million + (a million/2)x – a million/4 L(x) = (a million/2)x + 3/4 sqrt(0.9) ~~ L(0.9) = (a million/2)(0.9) + 3/4 = a million.2 sqrt(0.ninety 9) ~~ L(0.ninety 9) = (a million/2)(0.ninety 9) + 3/4 = a million.245

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