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An object is moving along the parabola y = 3x^2. (a) When it passes through the point (2,12), its horizontal velocity is dx/dt = 3. what is its vertical velocity at that instant? (b) If it travels in such a way that dx/dt = 3 for all t, then what happens to dy/dt as t --> +infinity? (c) If, however, it travels in such a way that dy/dt remains constant, then what happens to dy/dt as t --> +infinity?

  • calculus -

    What was wrong with my previous response? I still make no sense of the last part.

  • calculus -

    For question a, y = 3x^2, so
    dy/dt = 6x dx/dt
    dy/dt = 6(2) * 3
    dy/dt = 36

    For question b, as t approacing infinity, x is also approaching infinity (the object is moving along the track of the function, remember(, then dy/dt is also approaching infinity in vertical sense...

    For question c, I think you ask for dx/dt, instead of dy/dt since dy/dt always constant... If you ask for dx/dt, dx/dt will be approaching 0 as dt approaching infinity. This is the reason:
    dy/dt = 6x dx/dt
    as t approaching infinity, x will also be approaching infinity.. Since we hold dy/dt to be constant, dx/dt will have to be a small number to counter the growth of 6x as it approaches infinity.. Therefore, dx/dt will have to approach 0

    Hope it helps

  • calculus -

    No, nothing was wrong with your last response. That was my mistake for posting it up again. Thank you for all your responses.

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