Find the linear approximation of the function f(x)= sqrt (4-x) at a=0 Use L(x) to approximate the numbers sqrt (3

Math Jan 18, 2021

Find the linear approximation of the function f(x)= sqrt (4-x) at a=0

Use L(x) to approximate the numbers sqrt (3.9) and sqrt (3.99) Round to four decimal places

Expert Solution

L(x) = 2 - 1/4(x)

since you are looking for v3.9, substitute x = 0.1, so that 4 - 0.1 = 3.9

L(0.1) = f(3.9) = 2 - (0.1/4)

= 1.975

now substitute x = 0.01

L(0.01) = f(3.99) = 2 - (0.01/4)

= 1.9975

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