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Math Help - Tangent answer not agreeing with calculator?

  1. #1
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    Tangent answer not agreeing with calculator?

    Hi again, all! I worked out the velocity of this curve s= t^2 - 8t + 18 at t = 4 to be 2 m/s, but the graph on my calculator really doesn't look like the instant v at t = 4 is anywhere near 2 (looks like zero). So I tried to write out the general formula for this and am not sure my next step, any hint would be valued

    lim h -> 0 (a^2 + 2ah + h^2 - 8a - 8h + 18) / h

    There's nothing to cancel out so how can I make this into a workable limit?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by DannyMath View Post
    Hi again, all! I worked out the velocity of this curve s= t^2 - 8t + 18 at t = 4 to be 2 m/s, but the graph on my calculator really doesn't look like the instant v at t = 4 is anywhere near 2 (looks like zero). So I tried to write out the general formula for this and am not sure my next step, any hint would be valued

    lim h -> 0 (a^2 + 2ah + h^2 - 8a - 8h + 18) / h

    There's nothing to cancel out so how can I make this into a workable limit?
    What you have is equivalent to saying \lim\limits_{h\to 0}\dfrac{f(a+h)}{h} which is incorrect. You didn't subtract off that value of the function at a! If you evaluate \lim\limits_{h\to 0}\dfrac{f(a+h)-f(a)}{h}, you will get the desired cancellations. Then plug in a=4 (you could actually do this from the start..makes calculations a tad easier to do).

    Can you proceed?
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  3. #3
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    I will first quote Homer Simpson: D'oh!

    I will then quote Dr. Farnsworth: Huzzah!

    I will then compliment both of your mini animations, which did indeed give me the chuckles. Good day to you, sir!
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