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Unformatted text preview: NATIONAL UNIVERSITY OF SINGAPORE Department of Mathematics MA 1505 Mathematics I Tutorial 6 1. Imagine you are visiting a country in the winter season. Let T ( x,y ) = 36- 1 5 [ x 2 + ( y- 5) 2 ] be the temperature at location ( x,y ) in a 10ft × 10ft hotel room with a heater on at night. One corner of the room is at (0 , 0) and the opposite corner is at (10 , 10). (i) What is the domain of the temperature function? (ii) Where is the likely location of the heater? (iii) Suppose you like to sleep within the temperature range of 20 ◦ C to 25 ◦ C. Where would you put your bed? (iv) Determine the locations in the room where the temperature is lowest. Ans . (ii) (0 , 5); (iv) (10 , 0) and (10 , 10). 2. In an electric circuit, the voltage of V volts (V), current of I amperes (A), and resistance of R ohms (Ω) are governed by Ohm’s Law V = I × R. (i) If the resistance is fixed at 15 Ω, how fast is the current increasing with respect to voltage?...
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