# How fast is the volume changing with respect to time when the radius is changing with respect to time when the radius is changing at a rate of dr/dt=1.5 feet per second and r=2 feet?

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To find how fast the volume is changing with respect to time when the radius is changing at a rate of ( \frac{dr}{dt} = 1.5 ) feet per second and ( r = 2 ) feet, you can use the formula for the volume of a sphere, ( V = \frac{4}{3} \pi r^3 ), and differentiate it with respect to time using the chain rule. Then substitute the given values for ( r ) and ( \frac{dr}{dt} ) into the expression to find the rate of change of volume with respect to time.

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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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