Practice Problems-Solutions (1) - Practice Problems-Solutions Problem 1 Evaluate the following limit lim x0 1 1 2 x tan2 x Solution We combine the

Practice Problems-Solutions (1) - Practice...

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Practice Problems-SolutionsDecember 12, 2014Problem 1Evaluate the following limit:limx01x2-1tan2x.
Problem 2Evaluate the following limit:limx→∞(lnx)100x0.01.
Problem 3You put a cup of hot coffee with temperature 100Cinside an ice box with temperature 0C. 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 50C(in terms ofk)?(b) What is the cooling constantkif it took 10 minutes for the coffee to be 70C?Solution
Problem 4Prove a reduction formula (Relation betweenI(m, n) andI(m, n-2)) for the integral:I(m, n) =Zsinmxcosnx dx.

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