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(Solved): Suppose that f is differentiable at x_(0). Let L be the "best linear approximation" defined by L(x)= ...



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
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