OFDIFTERENTIAITON
4 APPLICATIONS
270 iii] CHAPIER
4.5 Exercises
to sketch the curve'
l-40 rtttUse the guidelines of this section
2,y--x3+6x2+9x
l'Y:x'+x
- xo
4' Y:8x'
3.y:2-15x+9x'-x3
6. Y: x(x + 2)3
5. y: x4+ 4x3
l , Y : 2 x s - 5 x z+ t
*
9 . 'y :
.I
8.Y:20x3-3x5
x
1 0 y. :
x-
13.y:
xr_g
x
'y:
the force of attractionbetwe
42. Coulomb's Law statesthat
14.y:7+g
particles i s directlvp:"p".{"i,11t: :T^tt^t-ill
charged
to.thesquareof the
x2-2
16.y : --7-
uifo.itio^
x'
andinverselyproportional
ffi.,
char.ge
them.Ttrefigureshowsparticleswith
betw"een
xr+g
x-l
15. 'yx :- ----;ll.
A:T
12.y:h
1
ll.y:
1 9 .y : * t E - ,
wherekisapositiveconstant.Sketchthegraphoft}rc
about the force?
function. What does the graph say
24.y: xJ277
-r L
,E=7
2 6 .'v : - - -
25. .t-: ----
^
x
lx'-
L
28.y-xslz-5x213
2l.Y:Y-J7rt3
29.y:x+VTil
30.r : il7r=-ff
slant asymptote'Do not
43-46 rrrrFind an equation of the
the curve.
xz+l
43.-v: ----.-,
x-f r
3l.Y:3sinx-sin3't
4 4 .'
q 6 .Y -
4x3-2x2t5
-Tl2 < x < nlL
33. y : xtanx,
-n l z 1 x I n l 2
34. y : 2x - ta n x ,
35.y:lx-sinx,0(x13n
36. y : c o s 2-t Z s i n x
s i n 2 x- 2 s i n x
2x3+x'+x
V-
45.v:-r*+x-3
32.Y:sinx-tarx
sinx
39. "v : -,-- | +cosx
o<x<2
F ( x )-: + . C %
20.y:2$-*
21.y: ^lEzT1 x
37.y :
the net
ffir."*;i#ttut
is
x--rl
x--fJ
a particle
0 and z uln acoordinate line and
ft:*
x between
ilree -! ataposition
llt:ll"::ii;
force actingon themiddle
xr_t
18. 'v : --;-:-
x'
--;--:=
2 3'v. : - lx.
+
(E is Young's
where E and 1 are positive constants'
inertia o! a croLl
elasticity and / is th" to-"ttt of
deflection curve'
the
of
itr" U"u*.) Sketch the graph
a
.
^
x'+/,x
5xa+x'+x
* z - x 2* 2
E O
section to sketchthe
47-52 ttlt Use the guidelines of this
slant asymptote'
guideline D find an equation of the
3 8 ' Y : si nx x
cos 'r
40.y : tT.'i*;
o n o o
length L embeddedin concrete
41. The figure shows a beam of
evenly along its
walls. If a constant load IV is distributed
curve
deflection
the
of
length, the beam takes the shape
wL ^ - wL' '',--,
w
*
t[EI
I',EI'24EI'-
47, v*:
-2x2+5x-r
x-
Zx-l
50.xY:72+x*l
49.xY:12 + 4
5i. 'y:
2x3+x'+l
-----;
,-1x-'T
x2+12
48. 'v : --------L
L
(x + 1)3
52. 'y : ------r,z
- rJ
t.r
: J47 + g has two slantasyt
53. Show that the curve y
-2x'rJsethis
fact to help sketchthe
:
! : 2xand y