# How do you find instantaneous velocity in calculus?

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To find instantaneous velocity in calculus, you use the derivative of the position function with respect to time. Mathematically, if ( s(t) ) represents the position function, then the instantaneous velocity ( v(t) ) at time ( t ) is given by the derivative ( v(t) = s'(t) ). Alternatively, if the position function is given as ( s(t) ), you can find the instantaneous velocity by determining the limit as the time interval approaches zero of the average velocity over that interval, which is expressed as ( v(t) = \lim_{\Delta t \to 0} \frac{s(t + \Delta t) - s(t)}{\Delta t} ).

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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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