Find the linear approximation of the function f(x) = √4-x at a = 0 and use it to approximate the numbers √3.9 and √3.99 ? (Round your answers to four decimal places.)

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Answer 1 · 2017-12-21T16:37:57

Use the Taylor form:

#f(x)=f(a)+(x-a)*f'(a)....#

#f(x)'=(sqrt(4-x))'=1/2(-1)/sqrt(4-x)#

#f(0)=sqrt(4-0)=2#

#f(0)'=1/2(-1)/sqrt(4)=-1/4#

#sqrt(3.9)=f(x)~~ 2+0.1(-1/4)=1.9750#

#sqrt(3.99)=f(x)~~ 2+0.01(-1/4)=1.9975#