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Math Help - secant

  1. #1
    Senior Member euclid2's Avatar
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    secant

    Determine an expression, in simplified form, for the slope of the secant PQ

    a) P(1,3), Q(1+h,f(1+h)), where f(x)=3x^2

    Now, i know which formula to use, which is

    Limh->0 \frac{(x+h)-f(x)}{h}

    i have the solution to this problem, but don't understand where the numbers are coming from so it's useless to me. i don't understand how to plug the numbers into this formula

    for the first step it is:

    Limh->0 \frac{3(1+h)^2-3}{h}<br />

    then simply simplifying to get

    3h+6

    can someone please explain this to me?
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  2. #2
    Super Member Deadstar's Avatar
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    Quote Originally Posted by euclid2 View Post
    Determine an expression, in simplified form, for the slope of the secant PQ

    a) P(1,3), Q(1+h,f(1+h)), where f(x)=3x^2

    Now, i know which formula to use, which is

    Limh->0 \frac{(x+h)-f(x)}{h}

    i have the solution to this problem, but don't understand where the numbers are coming from so it's useless to me. i don't understand how to plug the numbers into this formula

    for the first step it is:

    Limh->0 \frac{3(1+h)^2-3}{h}<br />

    then simply simplifying to get

    3h+6

    can someone please explain this to me?
    Formula should be \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}

    You're taking x=1 and hence 1+h.

    So f(1) = 1 and f(1+h) = 3(1+h)^2.

    Hence, \lim_{h \to 0} \frac{f(1+h)-f(1)}{h} = \frac{3(1+h)^2 - 3}{h}= \frac{3h^2 + 6h}{h} = 3h + 6 = 6 as h \to 0
    Last edited by Deadstar; April 12th 2010 at 04:05 PM. Reason: fixed various errors
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  3. #3
    Senior Member euclid2's Avatar
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    Quote Originally Posted by Deadstar View Post
    Formula should be \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}

    You're taking x=1 and hence 1+h.

    So f(1) = 1 and f(1+h) = 3(1+h)^2.

    Hence, \lim_{h \to 0} \frac{f(1+h)-f(1)}{h} = \frac{3(1+h)^2 - 3}{h}= \frac{3h^2 + 6h}{h} = 3h + 6 = 6 as h \to 0
    so what you're doing is plugging (1+h) into 3x^2 to get 3(1+h)^2 ??

    and thanks for the help!!
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  4. #4
    Super Member Deadstar's Avatar
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    Quote Originally Posted by euclid2 View Post
    so what you're doing is plugging (1+h) into 3x^2 to get 3(1+h)^2 ??

    and thanks for the help!!
    Yeah, see what I think is going on in the question is you are being asked to find the slope of the curve at the point (1,3).

    Now you can do this simply by differentiating f(x) (= 6x) and plugging in x=1.

    But it seems they want you to use the formula...

    \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}

    Read this to learn more.
    Derivative - Wikipedia, the free encyclopedia

    Since we are using x=1 (as in P(1,3)).

    Plug x into the above formula and just expand it.
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