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

For the parametric function the derivative is given by

rewriting as a single fraction.

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To differentiate the parametric equations (x(t) = t\sqrt{t^2 - 1}) and (y(t) = t^2 - e^t), you can use the chain rule. Differentiate each equation with respect to (t) separately to find (dx/dt) and (dy/dt), which represent the rates of change of (x) and (y) with respect to (t), respectively.

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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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