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

Sec. 31 Limits 31
269. a)
270. lim-^4i; a)
' Hm-^-; x~ *
Construct the graphs of the following functions:
271**. y = \im (cos 2
"*).
n->oo
272*. y=lim
n-*c
*
* i x
273. y = \im J/V-t-a 2
a->o
274. t/ = li;n|
275. t/ = li
-*<
n (x^O).
.
276. Transform the following mixed periodic fraction into
a common fraction:
a = 0.13555...
Regard it as the limit of the corresponding
finite fraction.
277. What will happen to the roots of the quadratic equation
if the coefficient a approaches zero while the coefficients b and c
are constant, and fc^=0?
278. Find the limit of the interior angle of a regular n-gon
as n > oo.
279. Find the limit of the perimeters of regular n-gons inscribed
in a circle of radius R and circumscribed about it as n - oo.
20. Find the limit of the sum of the lengths of the ordinates
of the curve
y = e~*cos nx,
drawn at the points x = 0, 1, 2, ..., n, as n *oo.
281. Find the limit of the sum of the areas of the squares
constructed on the ordinates of the curve
as on bases, where x=^l, 2, 3, ..., n, provided that n *oo.
282. Find the limit of the perimeter of a broken line M^.. .Mn inscribed in a logarithmic spiral