Suppose the temperature inside a three dimensional ball is proportional to the square root of the distance from the center. Find a formula for the average temperature in the ball. What is the limit of the average temperature as the ball gets larger?

The formula for the average temperature in the ball is . The limit of the average temperature for the ball does not exist.

Step-by-step explanation:

According to the statement, we have the following direct relationship:

(1)

Where:

- Temperature, measured in degrees Celsius.

- Distance from the center, measured in meters.

- Proportionality constant, measured in degrees Celsius per meter.

Under the assumption that ball is a continuous entity, we find that average temperature in the ball (), measured in degrees Celsius, is represented by the following integral equation:

(2)

By applying (1) in (2), we find that:

If the ball gets larger, then the limits associated to the average temperature diverges to the infinity as maximum exponent of the numerator of the rational function () is greater than the maximum exponent of the denominator (). Therefore, the limit of the average temperature for the ball does not exist.

answer: b

step-by-step explanation: