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Thread: Where to even begin with this piecewise monstrosity?

  1. #1
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    Where to even begin with this piecewise monstrosity?

    You don't really have to do these problems for me, but at least explain how to even comprehend this. Thanks!
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  2. #2
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    Re: Where to even begin with this piecewise monstrosity?

    This is all pretty straightforward

    $B(r) = \begin{cases}\dfrac{B_0}{r_0}r &r \leq r_0 \\r_0 B_0 \dfrac{1}{r} &r_0 < r \end{cases}$

    So we see that $B(r)$ is linear in $r$ for $r\leq r_0$ and is proportional to $\dfrac 1 r$ for $r > r_0$

    We also note that $B(r_0) = B_0$

    Given above it really should be pretty clear which graph corresponds to $B(r)$ (hint: C)

    Is $B(r)$ continuous at $r_0$? Well look at it. Is it? (hint: B)

    Does the derivative exist at $r_0$ It should be pretty clear that D is correct. Functions with kinks in them aren't differentiable at the kink.
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  3. #3
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    Re: Where to even begin with this piecewise monstrosity?

    Much appreciated.
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