Anonymous asked in Science & MathematicsMathematics · 8 years ago

True or false: if f'(r) exists, then lim x ->r f(x) = f(r)?

True or false

If f '(r) exists, then lim x->r f(x)=f(r)

Please give an explanation why.


1 Answer

  • 8 years ago
    Favorite Answer

    assume r is any number.

    {r ∈ ℝ}

    as x becomes sufficiently close to that number, f(x) becomes arbitrarily close to f(r).

    for example:

    say r = 7

    which means:

    f(r) = f(7)

    as x approaches r, x approaches 7.

    when you've decided that x is sufficiently close to 7 to verify the limit to yourself, plug that x value (something damn near 7) into f(x) for x. you'll see that:

    f(x) = f(7ish)

    and remember that:

    f(r) = f(7)

    so by transitive property,

    f(x) = f(r)

    this is not a proof though. It's just an example to help verify the theorem.

    so anyway,

    the answer is True.

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