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

Answers 411
down; [7^, oo Y concave up; M f ^= _JL is a ) point of ; [7^, inflection.
oo Y concave up; M f ^= _JL is
)
V/> J (Y* W)
899. ( oo, 0), concave up; (0, oo), concave down; 0(0, 0) is a point of
inflection. 900. (00, 3) and (1, oo), concave up; (3, 1), concave
down; points of inflection are M l ( 3, T j
and M 2 ( 1,
J.
901. A' =
iy = 0. 902. *=1, x^=3, = 903. x= 2, y= 1. 904. = x. 905.0 = *,
left, = x, right. 906. = 1, left, = l, right 907. jc-= 1, y=-x, left,
= *, right 908. = 2, left, y-=2x 2, right. 909. 0^2 910. jt-=0.
0=1, left, = 0, right. 911. * = 0, 0=1. 912. i/^O. 913. *-=!.
914. = x n, left; y = JC + JT, right. 915. y a. 916. ma x = when x y
0;
min = 4 when x = 2\ point of inflection, Af,(l, ~~2 )- 917 - 1 ^/max^ when
jf=V r
3; m in r=: when jc = 0; points of inflection Ai l|f f 1, ~)
918. m ax == 4 when x = 1; ymin = Q when je=l, point of inflection, M, (0, 2).
919- f/max^ 8 wnen ^ = 2, //m in = when Jt = 2; point of inflection^ M (0, 4).
920. //min^ ! when A'^0; points of inflection M lt2 (Y5, 0) and
- \, 921 - ^max^ 2 when x^O; /ymin ^2 when x-=2; asymp-
totes, x 1, 0=-xl. 922. Points of inflection M, lt (l, T2); asymptote
x = 0. 923. max ~ ^ when x 1; f/mm 4 when i=l; AT asymptote, = O.
924. (farm = 3 when jc=l; point of inflection, M( 1/2, 0); asymptote,
x = 0. 925. 0max~'Q- wnen * = 0, points of inflection, M lt
- J \\
' (\ r
o
asymptote, = 926. #max-~ 2 when x--0; asymptotes, x--2 and y 0.
927. ym \ n ~ 1 when x = --J; m jx ==l whenx=l; points of inflection, 0(0, 0)
and Ai lf J2/"3, -^)'. asymptote, = 928. max =l when x-^4;
point of inflection, Ai(5, 77-]; asymptotes, x = 2 and 0. 929. Point
\ y / 97
of inflection, 0(0, 0); asymptotes, x =- 2 and = 0. 930. nnx = --,
8
'16
when jc^= -; asymptotes, x 0, x = 4 and = 931. f/max = 4 when
*--- 1; 0min = 4 vvnen x~\\ x = Q
asymptotes,
and = 3v 932. A (0, 2)
and /^(4, 2) are end-points; ma x = 2 V r
2 when ;c = 2 933. /I (8, 4) and
B (8, 4) are end-points. Point of inflection, 0(0, 0). 934. End-point,
A ( 3, 0); m in^= 2 when x = 2. 935. End-points, A(Y$* 0), 0(0. 0)
and B(Y$* 0); 0max= V% when jg= 1; point of inflection, M (1^3 -f 2 f^J,
Q l
V V + 936f
~YH
^nax^ 1 when x = 0, points of inflection,
M, t(l, 0). 937. Points of inflection, M l (Q t 1) and M f (1, 0); asymptote,
0=^ x. 938. max = when x = 1; m = 1
in (when x = 0) 939. max -=2
when x = 0; points of inflection, M 1>2 (1, K 2); asymptote, 0.
940. s m n = 4 when x = 4; max 4 wh'en x==4; point of inflection, 0(0, 0);
j ^ ~~
3 / ~~
asymptote, = 0. 941. ym \ n =y 4 when x = 2, 0mi n =K 4 when x = 4;
2 when x = 3. 942. m in = 2 when x = 0; asymptote, x=2.
943. Asymptotes, jc= 2 and = 0, 944. 0min^ T7= when
1/2
\
4 J