Suppose f(x) = 1/(1 + x) is to be approximated near x = 0. Find the linear approximation to f at 0. Then complete the following table showing the errors in various approximations. Use a calculator to obtain the exact values. The percent error is 100|approximation - exact|/|exact|. Comment on the behavior of the errors as x approaches 0.

Linear approx. Percent error Exact value 0.1 0.01 0.001 0.0001 -0.0001 -0.001 -0.01 -0.1