# What is the instantaneous velocity of an object moving in accordance to # f(t)= (t^2sin(t-pi),tcost) # at # t=pi/3 #?

We also know that

Again, differentiate with the product rule.

The derivative of the entire parametric equation is found as follows:

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The instantaneous velocity of the object at ( t=\frac{\pi}{3} ) is ( v(t)=(-\frac{\pi}{3}\sqrt{3},\frac{\pi}{3}) ).

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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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