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

_Answers_413
Ji 5
* = ' T ^nin = 1 When * = ; ymax =^- 7 l wnen * = 5 f
#min = 1 when
=l when * = 2n; points of inflection, Ai^O.36, 0.86);
M 2 (1.21, 0.86); M,(2.36, 0); M 4 (3.51, 0.86); M 5 (4.35, 0.86);
V~2
A4 e (5.50, 0). 963. Periodic function with period 2n. ym \ n = L ~ when
when * = ji + 2foi (fc = 0, 1, 2, ...);
3
asymptotes, x=-r-Ji + ^Jt 964. Periodic function with period n; points of
inflection, M k ^ + kn, -y- J (fc = 0, 1, 2, ...); asymptotes, * = JI+/JJT. j
965. Even periodic function with period 2n On the interval [0,
= when ^ = rr^s t/max = 0whenx-n;t/mln = - ^= when
arccos-^;
c = arccos (
-- 7=)' ^min = wnen ^==0; points of inflection, M l ( ,
Af skill:?,
; M - t
8
, 966. Even
(arc lO^ (jt^arcsin J^ ^-)
periodic function with period 2it. On the interval [0, n] t/ma x 1 when
= -F= when x = arccos -=. ; ^min=--F-
Oj ;
vvhen
A: = arccos ^zr ; (/m i n = 1 when x^Ji; points of inflection, M! f
-y ,
Oj;
-.(/S-i/S)' (- (-/I)- -i/g)-
967. Odd function. Points of inflection, M* = (fcjt, fejt) (/j 0, 1, 2, ...).
968. Even function. End-points, 4, 2 (2 83, 1 57) 1 t/max^ 57 when A: =
(cusp); points of inflection, Af
lf J(1.54 t 0.34). 969. Odd function.
Limiting points of '
graph ( 1, oo) and (1, + oo). Point of inflection,
0(0, 0); asymptotes, x\. 970. Odd function. t/max =
-^q
O
1 + ?JT when
x -j- + /en; /m in = n + 1 +2^n when A; = -J JI + /JJT; points of inflection,
2k 4- 1
M k (kn, 2fcrc); asymptotes, x^-y 1-^ (6 = 0, 1, 2, ...). 971. Even
function, t/mln^ when x = 0; asymptotes, (/ = -^-^
1 (as x-* oo) and
// =^.^1 (as *-*+oo). 972. (/m | n = when x = (node); asymptote, y = l.
1 +-fr
when JC==1; ^max= " -- 1 Whe" X=S ~" I; Point J
inflection (centre of symmetry) (0, Ji); asymptotes, y = x + 2n (left) and y = x
(right). 974. Odd function. t/min=1.285 when JC=1; t/max = 1.856 when
#== l; point of inflection, M f 0, -^- j
; asymptotes, t/ = -- + ji (when
y
^-^ oo) and y = -^ (as ^-^+00). 975. Asymptotes, # = and # = * In2.