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agentx5

  • 3 years ago

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x = t − t\(^{−1}\), y = 6 + t\(^2\), t = 1 The correct answer needs to be in the form of y=something... I have this (incorrect): \[y=(\large\frac{2t^3}{t^2+1})x+7\] @ t=1, x=0 and y=7 \(\large\frac{dy}{dt}\)=2t \(\large\frac{dx}{dt}\)= 1+\(\large\frac{1}{t^2}\) = \(\large\frac{t^2+1}{t^2}\) Dividing by something, same as the product of its reciprocal, when doing \(\frac{dy}{dx}\) Where's the error?

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  1. agentx5
    • 3 years ago
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    Fixed the typo with the fraction command, press F5 to refresh and make it display properly. Am I understanding this question right @TuringTest ?

  2. TuringTest
    • 3 years ago
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    It's looking correct to me...

  3. TuringTest
    • 3 years ago
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    except that you can plug in the value for t... which just makes y=x+7

  4. agentx5
    • 3 years ago
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    Wait what? You mean just plug in 1?

  5. agentx5
    • 3 years ago
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    Ooooh!

  6. TuringTest
    • 3 years ago
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    why not, you need to know the value of the slope at that point, no?

  7. agentx5
    • 3 years ago
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    2/2 = 1 and it goes away

  8. TuringTest
    • 3 years ago
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    yeah, is that right? do you know?

  9. agentx5
    • 3 years ago
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    lol that was it /facepalm at myself >_<

  10. TuringTest
    • 3 years ago
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    haha sweet, it happens :)

  11. agentx5
    • 3 years ago
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    Well everybody got to see my work then lol

  12. myko
    • 3 years ago
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    i can't really read well your solution, but it is done like this: find point value for t=1, which is (0,7) find tanget vector at t=1 which is (2,2) write the equation: (x,y) = (0,7)+v(2,2) from here you can write it in the form y=something by eliminating v

  13. agentx5
    • 3 years ago
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    Ty myko :-) Yeah that's basically my steps too I'm doing... 1. find dy & dx with respect to dt (derivative of both) 2. find dy/dx 3. find the point for when t is as given, the x & y coords 4. put in the form of y=mx+b, solve for b using the known x & y 5. rewrite y=mx+b

  14. myko
    • 3 years ago
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    my way is shorter, :). You can avoid step 2. But ya, good job

  15. myko
    • 3 years ago
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    no need of that, becouse actually sometimes it will not work, if the dy/dx is infinity for example

  16. myko
    • 3 years ago
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    just keep y and x same level variables without considering one of them like the independent one till the end

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