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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`