Let f (x )equals x squared and note that Modifying Below lim With x right arrow 2f(x)equals 4. For epsilon equals 1, use a gra
phing utility to find the maximum value of delta greater than 0 such that StartAbsoluteValue f (x )minus 4 EndAbsoluteValue less than epsilon whenever 0 less than StartAbsoluteValue x minus 2 EndAbsoluteValue less than delta.
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Answer:
The water level is rising at a rate of approximately 0.1415 meters per minute.
Step-by-step explanation:
Water is flowing into a right cylindrical-shaped swimming pool at a rate of 4 cubic meters per minute. The radius of the base is 3 meters.
And we want to determine the rate at which the water level of the pool is rising.
Recall that the volume of a cylinder is given by:
Since the radius is a constant 3 meters:
Water is flowing at a rate of 4 cubic meters per minute. In other words, dV/dt = 4 m³ / min.
Take the derivative of both sides with respect to <em>t: </em>
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Implicitly differentiate:
The rate at which the water level is rising is represented by dh/dt. Substitute and solve:
Therefore:
In conclusion, the water level is rising at a rate of approximately 0.1415 meters per minute.