Use linear approximation, i.e. the tangent line, to approximate 1/0.103 as follows: Let f(x)=1/x and

Question

Use linear approximation, i.e. the tangent line, to approximate  as follows: Let  and find the equation of the tangent line to  at a "nice" point near . Then use this to approximate .

Answer 1

"Nice" point: (.1 , 10) ; f^'(x) = -1/x² ; f^'(.1) = -100 ; f(.103) ~ 10 - 100(.003) = 9.7