Problems in Mathematical Analysis.pdf - pwp.net.ipl.pt

Answers
(2, oo), increases. 824. ( 00, a) and (a, oo), decreases.' 825. (00, 0) and
(0, 1), decreases; (1, oo), increases 827. ymax = j when * = -
409
. 828. No
-
extremum. 830. t/m in = when x=Q; t/mln=0 when x= 12; t/max = 1296 when x = 6.
831. t/min^ 0.76 when x=5=0.23; i/max = when x= 1; t/mfn
=^ 0.05 when
x=^1.43. No extremum when x = 2. 832. No extremum. 833. #max = 2
9
when *=0; |/m i n = 2 when x = 2 834. #max = yg when x = 3.2. 835. t/max =
= 3/3 when x=
^L; f/min = 3/3" when 836. r/max =
^==^ /2
yO r 5
when x = 837. j/max = V"3 when x = 2^3; ymin = K^3" when x = 2K r
".
838. i/mm -0 when *=1; (/ma x = l when x = 839. ymta = s/"3 when
9rr
840. [/m ax-= 5 when ^= 12 ^n; ^/max^^cos when x=1
= Scos^when *=12 fjkJ:^ Ji; ymin=l when x = 6 (2fe + 1) JT (fe-^0,
1, 2, ...). 841. ymln ==0when x = 0. 842. ymln = - - when x = -.
843. t/max^^- w^n x = ~;//min ==0 when x=\ 844. f/m?n -l when
1
x = 845. ymln = - when x = 1. 846. f/mln = when x = 0; //max--2
c
*,
when x = 2 847. f/min = g when x=l. 848. No extremum. 849. Smallest
value is m = 75-
2
for x~ 1; greatest value, M = 7rwhen x \. 850. m
when x = and x = 10; M = 5 for x = 5. 851. m=~ when x = (2fc -f- 1) -j- ;
fcjT
Af = l for x = j- (fc^O, 1, 2, ...). 852. m^=0 when x = l; M=JI when
x== _l. 853. /n=s l when x = 1; M = 27 when x = 3. 854. a) m- 6
when x=l; M=-^2o6 when x = 5; b) m = 1579 when x = 10; M = 3745 when
x=12. 856. p = 2, Isosceles. 864. The
side adjoining the wall must be twice the other side 865. The side of tlit
cut-out square must be equal to
base. 867. That whose altitude is equal
-g-
. 866. The altitude must be half the
to the diameter of the base
868. Altitude of the cylinder, -^L ; radius of its base R ]/ , where i<
y 3 ro __
is the radius of the given sphere. 869. Altitude of the cylinder, RV'2
where R is the radius of the given sphere. 870. Altitude of the cone,
--
4