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Math Help - Derivative Quiz Tomorrow

  1. #1
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    Sep 2008
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    Derivative Quiz Tomorrow

    Hey all, just doing some homework in preparation for the quiz tomorrow (well, today...it's in 4 hours).

    Running into trouble with using limits to compute derivatives.

    Here are the problems:

    Use limits to compute the following derivatives:

    1. f'(3) where f(x)=\frac{1}{2x-5}

    Pretty sure limit here is zero, but I do not understand how I would visualize this with much harder equations...

    2. f'(2) where f(x)=x^3

    3. f'(4) where f(x)=\sqrt{2x-1}

    Also confused about questions asking to compute limits that involve infinity:
    1. \lim_{x \to \infty}\frac{1}{x^2}

    2. \lim_{x \to \infty}\frac{5x+3}{3x-2}

    3. \lim_{x \to \infty}\frac{x^2+x}{x^2-1}

    Read the textbook a few times but cannot seem to grasp it... Would appreciate some help or at least a guide that is easy to comprehend.

    Another concern is the +'s and -'s atop of infinity. As far as I understand, these signify which direction to count the limit from. Anymore help would be greatly appreciated!
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  2. #2
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    Joined
    Aug 2008
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    Hope this helps

    Hi VX-1

    Finding solutions to the derivatives 2 and 3 isn't difficult but if you're being asked to solve them using limits thats a different story, the thing I used to do when solvin limits was substitute x - infinity with x = a very large number;

    For example 1.

    if we think of x being a very large number say 100000, then substitute it and solve it the answer is 1x10^-10 or effectively zero, we can say as x tends to infinity the limit is zero. (even though it is impossible to really divide by infinity)

    For question 2 we have a very large number divided by a very large number, adding 3 or subtracting 2 would have a negligible effect, the answer is close enough to 1 that we can say the limit is one.

    Hope that helped, good luck for your quiz
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