Suppose that
f
is differentiable at
x_(0)
. Let
L
be the "best linear approximation" defined by
L(x)=f(x_(0))+
f^(')(x_(0))(x-x_(0))
. Given that
R(x)=f(x)-L(x)
, show that
\lim_(x->x_(0))(R(x))/(x-x_(0))=0