This is actually a physics problem, but since my question is really about the math involved, I decided to post it in the calculus subforum.(adsbygoogle = window.adsbygoogle || []).push({});

I'm supposed to get from the term:

$$\lim_{\Delta t → 0} |\vec{v}_r (t + \Delta t)| \frac{\sin \Delta \theta}{\Delta t}$$

To:

$$v_r (t) \frac{d\theta}{dt}$$

##\theta## is a function of ##t## (so ##\Delta \theta## approaches zero as ##\Delta t## approaches zero), and ##v_r## is the scalar component (not the magnitude) of the vector ##\vec{v}_r##, in a particular direction.

Computing the limit as ##\Delta t## approaches zero:

$$\lim_{\Delta t → 0} |\vec{v}_r (t + \Delta t)| \frac{\sin \Delta \theta}{\Delta t} = |\vec{v}_r (t)| \frac{d\theta}{dt} = |v_r (t)| \frac{d\theta}{dt}$$

How do I get rid of those absolute value bars?

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# Limits involving absolute values

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