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How do you differentiate the following parametric equation: # x(t)=t-5, y(t)= t^2#?

Answer 1

William Abdalla

#2t#

#(dx)/(dt)=1 => (dt)/(dx)=1#

#(dy)/(dt)=2t#

#(dy)/(dx)=(dy)/(dt)xx(dt)/(dx) = 2txx1=2t#

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Answer 2

Cameron Alexander

To differentiate the parametric equations (x(t) = t - 5) and (y(t) = t^2), you would differentiate each equation with respect to (t) separately:

[ \frac{dx}{dt} = 1, \quad \frac{dy}{dt} = 2t ]

So, the derivatives of (x(t)) and (y(t)) with respect to (t) are (1) and (2t), respectively.

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Answer from HIX Tutor

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.