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3-78.

The position of a ball as a function of time is given by the function below where is in meters and is in seconds. Homework Help ✎

  1. Use your calculator to approximate the instantaneous velocity of the ball at and seconds.

    Instantaneous velocity = Instantaneous Rate of Change (IROC) = Derivative

    Rewrite  using exponents: 

    Find using the Power rule.

    Evaluate and .

  2. What happens to the velocity of the ball after a very long time (i.e. as )?

    Note: seconds is a very long time for a ball to be in motion. (This must be an unearthly situation!) Is increasing, decreasing or neither as ? Is  changing rapidly or not so rapidly? Explain.

  3. What happens to the position of the ball after a very long time, (i.e. what is)? Does this make sense given your answer to part (b)?

    Does a square root function (such as s(t)) have a horizontal asymptote as t→∞?