Mistakes regarding parametric curves: Difference between revisions
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(Created page with "* Sometimes people go on with rules without thinking and do this: <math>y = x^2 \to y(t) = t^2</math> and <math>x = \sqrt{y} \to x(t) = \sqrt{t}</math> which is to randomly do computations without knowing what it means. The graph of <math>(\sqrt{t}, \ t^2)</math> is half a parabola because of the square root and is also a distorted parabola because the horizontal coordinate does not have a constant rate of change.") |
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* Sometimes people go on with rules without thinking and do this: <math>y = x^2 \to y(t) = t^2</math> and <math>x = \sqrt{y} \to x(t) = \sqrt{t}</math> which is to randomly do computations without knowing what it means. The graph of <math>(\sqrt{t}, \ t^2)</math> is half a parabola because of the square root and is also a distorted parabola because the horizontal coordinate does not have a constant rate of change. | * Sometimes people go on with rules without thinking and do this: <math>y = x^2 \to y(t) = t^2</math> and <math>x = \sqrt{y} \to x(t) = \sqrt{t}</math> which is to randomly do computations without knowing what it means. The graph of <math>(\sqrt{t}, \ t^2)</math> is half a parabola because of the square root and is also a distorted parabola because the horizontal coordinate does not have a constant rate of change. | ||
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Latest revision as of 23:57, 12 November 2025
- Sometimes people go on with rules without thinking and do this: [math]\displaystyle{ y = x^2 \to y(t) = t^2 }[/math] and [math]\displaystyle{ x = \sqrt{y} \to x(t) = \sqrt{t} }[/math] which is to randomly do computations without knowing what it means. The graph of [math]\displaystyle{ (\sqrt{t}, \ t^2) }[/math] is half a parabola because of the square root and is also a distorted parabola because the horizontal coordinate does not have a constant rate of change.
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