# What is the derivative of #f(t) = (t^2-1 , t^2+1 -e^(2t^2-2) ) #?

This is parametric form of equation. In parametric form of equation,

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The derivative of ( f(t) = (t^2 - 1, t^2 + 1 - e^{2t^2 - 2}) ) with respect to ( t ) is ( f'(t) = (2t, 2t - 4te^{2t^2 - 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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- What is the arclength of #(t^2-t,t^2-1)# on #t in [-1,1]#?
- What is the arclength of #(t^2lnt,(lnt)^2)# on #t in [1,2]#?

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