# How do you differentiate the following parametric equation: # x(t)=t-e^(t^2-t+1)/t, y(t)= t^2-e^(t-t^2)#?

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To differentiate the parametric equations (x(t)) and (y(t)):

- Differentiate each equation with respect to (t).
- Apply the chain rule whenever necessary.

Here are the derivatives:

[ \frac{dx}{dt} = 1 - \frac{2t^2 - 2t + 1}{t^2} e^{t^2 - t + 1} ]

[ \frac{dy}{dt} = 2t - e^{t - t^2} - 2te^{t - t^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.

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