# What is the derivative of #f(t) = (lnt, -3t^3+5t ) #?

We have

then

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The derivative of ( f(t) = (\ln t, -3t^3 + 5t) ) is ( f'(t) = \left(\frac{1}{t}, -9t^2 + 5\right) ).

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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.

- How do you differentiate the following parametric equation: # x(t)=lnt-t, y(t)=(t-3)^2 #?
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- What is the arclength of #(t-3,t+4)# on #t in [2,4]#?
- What is the arclength of #(t-3t^2,t^2-t)# on #t in [1,2]#?
- How do you find the range given x=3-2t and y=2+3t for -2 ≤ t ≤ 3?

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