Homework Soursea Find the local linearization of fx 114x near x0 fx b Usi
(a) Find the local linearization of
f(x) = (1)/(1+4x) near x=0
f(x)= ??
(b) Using your answer to (a), what quadratic function would you expect to approximate g(x) = (1)/(1+4x^2)
g(x)=??
f(x) = (1)/(1+4x) near x=0
f(x)= ??
(b) Using your answer to (a), what quadratic function would you expect to approximate g(x) = (1)/(1+4x^2)
g(x)=??
Solution
a) L(x) = f\'(x)(x - a) + f(a) f(x) = 1/(1+4x) f\'(x) = -4/(1+4x)^2 f(0) = 1 L(x) = -4/(1+4x)^2 * x + 1 L(x) = -4x/(1+4x)^2 + 1 b) g(x) = 1/(1+4x^2) 1/x^2 must be used to approximate g(x)
