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

The derivative of the parametric function is

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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)=e^(t^2-t) , y(t)=lnt #?
- How do you find parametric equation for given curve: Line of slope 8 through (-4,9)?
- How do you find an equation for the plane that contains the line with parametric equations #l=(8 - 7t, -5 - 2t , 5 - t)# and is parallel to the line with parametric equations #x=3 + t, y=-7 + 9t, z=8 - 6t#?
- How do you find the length of the curve #x=3t-t^3#, #y=3t^2#, where #0<=t<=sqrt(3)# ?
- What is the arclength of #(9t^3-2t^2+15,-2t^2-12t-1)# on #t in [-2,3]#?

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