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Math Help - A few questions involving limits

  1. #1
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    A few questions involving limits

    Having problems with a few of these, thanks for any help in advance.


    This one is to be answered in terms of the constants involved
    lim ((3/h)-(3/a))/(h-a)
    h->a


    lim (cos(x)-2)/(sin(x))
    x->0

    lim ((1/(h+3)^2)-(1/9))/h
    h->0

    Thanks Again
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  2. #2
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    Quote Originally Posted by casesam View Post
    Having problems with a few of these, thanks for any help in advance.


    This one is to be answered in terms of the constants involved
    lim ((3/h)-(3/a))/(h-a)
    h->a


    lim (cos(x)-2)/(sin(x))
    x->0

    lim ((1/(h+3)^2)-(1/9))/h
    h->0

    Thanks Again
    The first can be easily found by recognising it as being the derivative evaluated at x = a of the function f(x) = 1/x ......

    For the second, the limit is -oo since you have a form -1/0.

    For the third, you should recognise it as being the derivative evaluated at x = 3 of the function f(x) = 1/x^2 ......
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  3. #3
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    Quote Originally Posted by casesam View Post
    lim ((3/h)-(3/a))/(h-a)
    h->a
    In case you don't know derivatives yet I'll do the first one. The third one is worked out by a similar method.
    \lim_{h \to a} \frac{\frac{3}{h} - \frac{3}{a}}{h - a}

    Multiply numerator and denominator by ha to remove the complex fractions:
    \lim_{h \to a} \frac{3a - 3h}{ah(h - a)}

    Now do some factoring and you are done.

    -Dan
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