# An object's two dimensional velocity is given by #v(t) = ( tsin(pi/3t) , 2cos(pi/2t )- 3t )#. What is the object's rate and direction of acceleration at #t=5 #?

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To find the object's acceleration at t=5, calculate the second derivative of the position function with respect to time. The rate of acceleration at t=5 is given by the second derivative, and the direction is determined by the corresponding unit vector.

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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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