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

414 Answers
976. j/mi n =1.32 when *=1; asymptote, x = 0. 977. Periodic function with
period 2jt. t/min = -g-
when x=^-ji + 2&JT; t/max ^=e wnen * = ^- + 2;ri
(fc = 0, 1, 2, ...); points of inflection, M^ Urcsin
and A^ arc sin
/ i/^ UlA
g
+ 2/m, e 2
978. End-points, 4(0, 1)
^ + (2fe+l)n,e 2 I
and B(\, 4.81). Point of inflection, M(0.28, 1.74). 979. Points of inflection,
M (0.5, 1.59); asymptotes, # = 0.21 (as x -+ oo) and r/ 4.81 (as *-*-|-oo).
980. The domain of definition of the function is the set of intervals (2kn t
2/jJt-f-ji), where fc = 0, 1, 2, ... Periodic function with period 2ji.
t/max = when * = + 2&Ji (& 0, 1, 2, ...); asymptotes, x kn.
981. The domain of definition is the set of intervals
(2fc+-jrjJi
where k is an integer. Periodic function with period 2ji.
Points of inflection, M k (2fcji, 0) = (fe 0, 1, 2, ...); asymptotes,
x=
-^- + 2fejt. 982. Domain of definition, x > 0; monotonic increasing
function; asymptote, x 0. 983. Domain of definition, ]x 2/jn |