find linear approximation of f(x) = √(16 - x) at a = 0 and use it to approximate √15.9 and √15.99 rounded to four decimal places.
i dont know what im doing wrong. whenever i do it i get y - 0 = -8(x - 4) as my equation
i dont know what im doing wrong. whenever i do it i get y - 0 = -8(x - 4) as my equation
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So, the linear approximation of f(x) centered around x=a is given by:
f'(a)(x-a)+f(a). For this function,
f'(x)=-(1/2)(16-x)^(-1/2), and so,
f'(0)=-(1/8). Now, the linear approximation is
(-1/8)x+4, and evaluating this
at x=.1 and x=.01 gives us 3.9875 and 3.99875, which approximate 15.9^(1/2)
and 15.99^(1/2), respectively.
f'(a)(x-a)+f(a). For this function,
f'(x)=-(1/2)(16-x)^(-1/2), and so,
f'(0)=-(1/8). Now, the linear approximation is
(-1/8)x+4, and evaluating this
at x=.1 and x=.01 gives us 3.9875 and 3.99875, which approximate 15.9^(1/2)
and 15.99^(1/2), respectively.