Problem 3You put a cup of hot coffee with temperature 100◦Cinside an ice box with temperature 0◦C. Suppose that the cooling constant for coffee isk >0 per minute. Use Newton’s Law of Cooling tofind the following:(a) How long does it take to lower the temperature of coffee to 50◦C(in terms ofk)?(b) What is the cooling constantkif it took 10 minutes for the coffee to be 70◦C?Solution
Problem 4Prove a reduction formula (Relation betweenI(m, n) andI(m, n-2)) for the integral:I(m, n) =Zsinmxcosnx dx.