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    #1
    Tell me how you understand this question. I've removed the details of the calculation to focus on the language and how certain ideas should be expressed. I know it's a weird thing to ask so just try to answer how you can.

    Calculate __________ for each $v_1, v_2, v_3$ and $p(t)$.

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    #2
    I would interpret that as we are given some $f(v_1,v_2,v_3,p(t))$ and a list of possible values for the 4 independent variables for which we are to compute $f$.

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    #3
    I would interpret it as calculating some function $f(v, t)$ three times, using $v = v_1$, $v = v_2$, and $v = v_3$, with $p(t)$ being used inside $f(v, t)$. In other words, I read: Calculate $f(v, t)$ in terms of $p(t)$ for $v = v_1$, $v_2$, and $v_3$, for some $f$.


    But without the context of the actual calculation, it's hard to be certain, especially when the question is written in plain English like this. In formal notation, there would be no ambiguity, for instance, but in English, it could have many different interpretations.

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    #4 Thread Author
    Great responses guys but let me rephrase a bit. I'm really focused on the structure of questions that have the form "For each _________ and __." This came from a linear algebra question so let's try this:

    Calculate ________ for $1+t^2, 2-t+3t^2, 4+t$ and $p(t)$.

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    #5
    That strikes me as you are given an expression containing some $f(t)$, and the first 3 cases give you an explicit function definition for $f$, while in the last you are to use a general function. For example, suppose in a Calc I course, the student is instructed that for each given $f(t)$, that are to compute:

    $ \displaystyle \frac{d}{dt}\left(g^n(f(t)) \right)$ and so they would do the following:

    First, the student would find via the power and chain rules:

    $ \displaystyle \frac{d}{dt}\left(g^n(f(t)) \right)=ng^{n-1}(f(t))\cdot f'(t)$

    i) $ \displaystyle f(t)=1+t^2$

    $ \displaystyle \frac{d}{dt}\left(g^n(1+t^2) \right)=ng^{n-1}(1+t^2)\cdot(2t)$

    ii) $ \displaystyle f(t)=2-t+3t^2$

    $ \displaystyle \frac{d}{dt}\left(g^n(2-t+3t^2) \right)=ng^{n-1}(2-t+3t^2)\cdot(6t-1)$

    iii) $ \displaystyle f(t)=4+t$

    $ \displaystyle \frac{d}{dt}\left(g^n(4+t) \right)=ng^{n-1}(4+t)\cdot(1)$

    iv) $ \displaystyle f(t)=p(t)$

    $ \displaystyle \frac{d}{dt}\left(g^n(p(t)) \right)=ng^{n-1}(p(t))\cdot p'(t)$

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    #6 Thread Author
    Your post completely answers how you interpret this, so thank you! There are two interpretations that I see and I want to give it a little more time before I explain so I'll post tomorrow and clarify what's going on. Hopefully someone else can think of another example for this problem and interpret it as he or she sees it too.

    Here's one thing to ponder and again, sorry this is cryptic but I don't want to influence your thoughts too much:


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