If 1-y is used as an approximation to the value of 11+y, |y|<1, the ratio of the error made to the correct value is:

1965 AMC 12 Problem 18

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18.

1-y

is used as an approximation to the value of

\dfrac1{1+y},

|y|\lt1,

the ratio of the error made to the correct value is:

y

y^2

\dfrac1{1+y}

\dfrac y{1+y}

\dfrac{y^2}{1+y}

Subtract the approximation

1-y

from the correct value

Divide that error by

\frac{1}{1+y}

The error is

\frac1{1+y}-(1-y)=\frac{y^2}{1+y}.

Dividing by the correct value

\frac{1}{1+y}

gives the ratio

y^2.

Therefore, the correct answer is B.