The temperature in Northern Hemisphere is a function of Longitude , latitude and time and is represented as .

(a) What is the meaning of , and .

is the rate of change of the temperature with respect to Longitude with latitude and time fixed.

is the rate of change of the temperature with respect to Latitude with longitude and time fixed.

is the rate of change of the temperature with respect to time with longitude and latitude fixed.

(b) Honolulu has longitude of and latitude .

Measurements are made on January at .

Find the sign of .

As the longitude increases, the temperature also increases because the temperature increases as it moves towards west.

Hence, is positive.

Find the sign of .

As the latitude increases, the temperature also decreases because the temperature decreases as it moves towards North.

Hence, is Negative.

Find the sign of .

As the time increases, the temperature also increases because the temperature increases air blows out of the southwest.

Hence, is Positive.

(a)

is the rate of change of the temperature with respect to Longitude with latitude and time fixed.

is the rate of change of the temperature with respect to Latitude with longitude and time fixed.

is the rate of change of the temperature with respect to time with longitude and latitude fixed.

(b) is positive, is Negative and is Positive.