# What is the instantaneous velocity of an object moving in accordance to # f(t)= (sin2t-cos^2t,tantsect ) # at # t=(-pi)/12 #?

Instantaneous velocity is

As such instantaneous velocity is given by

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The instantaneous velocity of the object at ( t = -\frac{\pi}{12} ) is ( \left( 2\cos(2t) + \sin(t)\sec^2(t), \sec(t)\tan(t)\sec(t) \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.

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