Once again "the management " is happy to cooperate by supplying a place where answers supplied by students (along with comments and corrections, if necessary) will be posted. Students who supply material for this page will be credited using their initials. So please send answers, comments, and corrections. Graphs should be described as well as possible. This isn't supposed to be a complete description of solutions, but just a place where someone who has attempted the problems can check their final conclusions.
a) (-6 sin (2x)) e^(3cos(2x) (CREDIT: KG, 11/12/97)
b) (3x+1)/(x^3+5x+9) (CREDIT: JM, 11/11/97)
c) cos((x+1)/(x^2+2)) ( (-x^2-2x+2)/(x^2+2)^2) (CREDIT: KG, 11/12/97)
Management comment: this derivative is already "simplified" more than is required! The top of the second term could be left as 1(x^2+2)-2x(x+1) -- every time you touch an algebraic expression, you risk making an error!
d) -(2x+5y) / (5x-e^y-1) (CREDIT: BN, 11/16/97)
Problem #2: g'(2)=16 (CREDIT: KG, 11/13/97)
a) The area A of the rectangle is changing: (dA/dt) = 5(0.4) + 3(-0.5) = increasing at 0.5 ft sq/sec. (CREDIT: BN, 11/16/97)
b)The diagonal D of the rectangle is changing: (dD/dt) = -0.22295ft/sec which means it is decreasing at 0.22295ft/sec. (CREDIT: BN, 11/16/97)
b) f'(x)=0 when x=1/2. Increasing (f' > 0) in (-infinity,1/2) and decreasing (f' < 0) in (1/2,infinity) (CREDIT KG, 11/13/97)
a) the MAXIMUM value is 28 (it occurs at -2) and the MINIMUM value is (256)/(27) which is approximately 9.48 (it occurs at 4/3). (CREDIT TS, 11/15/97)
Management comment: please read the problem. While it is not too difficult to find the location of the relative min & max of Q, the problem asks for the minimum and maximum values of Q on certain intervals, NOT a list of its relative extrema in those intervals. Remember that intervals have endpoints which may give candidates for highest and lowest points (for example, consider the function x on the interval [0,1], which has NO relative extrema but does have max and min values on that interval!).
a) the limit when x --> infinity is 0 ; the limit when x --> - infinity is 0 (CREDIT: BN, 11/16/97)
b) the limit when x --> infinity is infinity; the limit when x --> - infinity is 0.(CREDIT: BN, 11/16/97).
c) the limit when x--> infinity is infinity (CREDIT: BN, 11/16/97); the limit when x --> - infinity is ???
d) the limit when x --> infinity is 1; the limit when x --> - infinity is -1. (CREDIT: BN, 11/16/97)