How do you change the parametric equation to cartesian equation #x = t^2 - 1# and #y = t^3#?
In this case
And so:
Which you can multiply out if required.
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To change the parametric equations (x = t^2 - 1) and (y = t^3) to Cartesian equations, you eliminate the parameter (t) by solving one equation for (t) and substituting it into the other equation. Here's how:
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From the equation (x = t^2 - 1), solve for (t): [ t = \sqrt{x + 1} ]
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Substitute this expression for (t) into the equation (y = t^3): [ y = (\sqrt{x + 1})^3 ]
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Simplify the equation: [ y = (x + 1)^{3/2} ]
So, the Cartesian equation representing the parametric equations (x = t^2 - 1) and (y = t^3) is (y = (x + 1)^{3/2}).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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