How do you differentiate the following parametric equation: # x(t)=lnt-t, y(t)=(t-3)^2 #?
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To differentiate the parametric equations ( x(t) = \ln(t) - t ) and ( y(t) = (t - 3)^2 ) with respect to ( t ), you can use the chain rule and basic differentiation rules:
[ \frac{dx}{dt} = \frac{d}{dt}(\ln(t) - t) = \frac{1}{t} - 1 ]
[ \frac{dy}{dt} = \frac{d}{dt}((t - 3)^2) = 2(t - 3) ]
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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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