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

412 Answers
1/~JT
f Q \
J/max = TT= when * = 3 I points of inflection, Af, [ 3, -n-l, 0(0, 0)
V 2 ^ J '
\ 3
3, -o- ; asymptotes, x=l 945. /m ) iD = -0-7= when x = 6; point
J ' /2
(3
of inflection, M /12, j^r=V, asymptote, x = 2 946. */max = when x=l; point
V /iooy
/ 2 \
of inflection, M I 2, ;
-j- asymptote, y = Q. 947. Points of inflection,
)
M, ( 3a, and 5- M ) 2 ( a, ;
) asymptote, y = 0. 948. 1111162 f/max wnen
6
/ i/"~ ~\
x = 4; points of inflection, M^J 8 ^ 2 ^ 2
, g 2
); asymptote, y = 0.
949. = // rnax 2 when >: = 0; points of inflection, M f
lf 2 1,
when jc=l; w min = when ^ = 0. 951. t/max^ -
J.
950. t/max
74 when ^e 2 ^ 7 39 *
point of inflection, M (e"'* ^14.39, 0.70); asymptotes, * = and # = 0.
952. /min= j- wnen ^ = -4=., point of inflection, M (-rr== ,
2
953. f/min = g when x = g; point of inflection, M ,
(e
y-+Q when x-*0. 954. f/max = -F ^0-54 when jc = -y
1
"""472)-
~V, asymptote, A:- 1;
1 ^= . 86;
/min = when * = 0; point of inflection, Ai f- 1^0.63; ^=0.37);
\ e e J
y -^ as *- 1+0 (limiting end-point). 955. ym{n = 1 when x= V 2; points
of inflection, M 1>2 (1.89, 1.33); asymptotes, x=*l. 956. Asymptote,
y = Q. 957. Asymptotes, = r/ (when x-+ + oo) and y = x (as x -
oo).
958. Asymptotes, x = , # = 0, # = 1; the function is not defined on the
interval -- ,0 .
959. Periodic function with period 2n. ym \n =
when jc = j n + 2Jfeji; t/max = ^2" when A:= j + 2A5Ji (fc = 0, 1, 2, ...);
points of inflection, M k ( -j- n + kn, Oj.
960. Periodic function with
o _ e q
period 2ji. ymln == ^3 when *= j Ji-f2/5Ji; /max = V$ when
x= ~+ 2fen (fe = 0, 1, 2, ...); points of inflection, M k (kn, 0) and
Nk fare cos f
~^-J+2fejx, yg )^l5j.
961. Periodic function with period 2xc.
i/max=l
On the interval [ ji, ji], t/max = when j x= ~; /min = 2 when
*=n; i/m = in when ^ = 0; points of inflection, M l 2 (0.57, 0.13) and
M, 4 ( 2 20, 0.95). 962. Odd periodic function with* period 2;i. On internal
[0, 2it], i/max= 1 when x = 0; /mln=0.71 f when * = *.
when