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Example:Let (a) Find the average rate of change of with respect to over the interval.(b) Find the instantaneous rate of change of with respect to at the point .
We havePut Again Put The average rate of change over the interval is (b) For Instantaneous Rate of Change: We havePut Now, putting then The instantaneous rate of change at the point is .
We havePut Again Put The average velocity over the interval is (b) For Instantaneous Velocity: We havePut Now putting The instantaneous velocity at is
Example:Use the formula for the area of a circle to find, (a) the average rate of which the area of a circle changes with as the radius increases form to .(b) the instantaneous rate at which the area of a circle changes with when .
We havePut Again Put The average rate of change from to is (b) For Instantaneous Rate of Change: We havePut Now putting The instantaneous rate of change at the point is . |

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