1. it
L-1 €6."^nrr & Dc=v
fi^A Gr- ^*DU rtl
x+E
551d1 cnl
6-ct+f[rro
x+5
= E'- QnD+3
oE ao rr3:-*a
g A*s:
'{^n tc!
, ou,;
ur2->'ft dr) oo
Lralh ryf+ {
5r*) i.q :
ef* 4Um
x+2 ?(- -b
E f t4
0t^ c
It frr,d Urn
a)2 x-3
A*
44*-4
-*
= _41
I
/
t
$
</--*--Z!.^-
i
i
j
I
2. t
eu.t:h01 '"
,lctrfi ot'. fi"d
,n,..-l ,
5c'tucf I cn 1
unn
{"4
2_
-><
- 6x+?
*-*b
2'/- +8
)t+1<
- 2-
-
-r(^- lO'Y t25
d-* 1-
-lr( - I
C},
1- dr
)
r)
I
€-
n
,(^- zx - D
D
t..
U rr)
x. -4
Lt rn
'X-t b
t
Lrm
{+6
rm
*4) t
"rC- I
-..IR- 5
s)
(12
-
-
t-T
q
Lir,^
x-> L
f,tm
G-,
g9GI"-,
x- 1
IUrn .
{"{ J_ C=+
a
oL
i
I
(L
r)
(
@
)
3. qwcI *nr L-, Jg
L/ C*oq a- L* 2
6 -21xL3
zt+i% 'N>3
{h!-
^pf(eabta
pa"t + the.t ,m
fr.A C9 L,tnq
u+-Q
ca^A a.o d'
ro-oor ed-jr Z-
Tr.un, JeU"n
"(+-f
fc G)_g Jto
px"o*eFur6
ns- U''"')L
'
' v(+3
+hq
fI
f"ad-/
(r6'n
4v
Joo= )("t n
dr.
t
th'e "i*ruqo-rl - 7
elDprucaehe6 - ? J**
p;'.* rt +he f*-*^
J"e E
; Lir',
T
"C
:t,t 9_
t
: Lrrn
-i-
ai-2'
@b)
o
D_G 5
t-l rn {,r-l
tl*> 2'
_'i-r.d*
61"i.):' L ;ftu"s
{-'i '
utq j"D dr.t l
x+*g_
i
I
i
4. $*frcrL"o fr^A
551
Urn
U"n
,roj t"o
3x +6
bx+b
_B
-71-4 +& Crt -
irn 3+ Yrt
"(-rtrO 6-, I /x
z
-
Urn ;
214 t oO
C=*
utD
Lir.t
'*-11 'O
3+ )* )t
m
6
u"o G Urn G1,
al-e t,O -''{41"O
q +n- im CJ I e
A-)1a
t,
t)
3to In
tL
e-o
&(
a-
.9
(.-
)
5. ) frnA6; $,"n
1*-+ - "O
4*-xB
2e{
al^
Q
a_
Urq D
at
x' 2s+
>L+ eD 1--3x
a_
1
x -L* rL
(,
-d,rli06'0.
Urn
:(-+ 1,o
-t eo
Cu>
Gd
1-)d
= jnn
at+ + "O
CL
yL
- 2:>( +
L /rx-?
=-t'O
!r
/>(
+5 -o
e+5 +
')
>(
+5 +'z(
6
Q*hcrn'. fir.A
4f*h +.6
+6
n
-x-
,L'^_
+E
Unr)
X--+'t'O
cfn i [-r tq
d-+ t rD
Urn
{-) + ,0
l
I
=
-l
"q
)(-, +
a.txa
rG
a,t
1E
,,
6. .= Urn
-ll.-l Jr r<l
L,t"n
Dt-" + oO
KAt
{ffi+-,3
tr/x3
1+-L +1-p1a
e)
rtc tl
q*efr,'cn: ffi",J
!
r
ln0
:{,*, +,O
3t)?C+6
*t
551*htcft: 5
.i"rt
q(*+"O
3
irn '
d- +"D
6yc
#+rf +;d._
3
--)L
+X
6
d_ +
35x) *Jr tjr,t
*4 +.,o
,2r
E>a 'r 7*
a
+
t-rro
zL-q +CI
q
5{
6f
, a-t_
+x7-rr
R T
I
z
,tjm
"yLjU
c---
D
+ -<'
x5
+.4 'to {r
I
O
-6c-
7. q.ft1wa St-aqi, 8bh
nsqq qftfr-t (-1,-l), f(x) rrfr.nE< Efr&nTd qtrq r
{fi x = /3,".t^ fv3)=-)-2=-4<o
"u, {/3)= /r- /r- /r, = %,
,. )t.
'T+t{rqe'qfr
Sg{{srs x qqr<rwsfi-+<q oRm
ln x.l
dx
'. 1; , rii r':,i.' . "
q"rq qfr6{rcffi ** dY
= o <Ftrst
dx
l+lnx=0,St{t y
+x
qrqF
{.rlx=y,"*#=o+(/"f.,,0
{9{i( x = X f**y c< eifrffi qrcq q<(qfr$.qlr
WY
Eqlqnq ))s qflq fi rq, *=% R*" y=J5sin;r+3cosx €K
qftqa qtce r [Plove that .r,=.6sin-r +3cos_l.has a maximum
raltre fbr.
^=%l
1i
l
y'r q3 qfr'ffi ftfg s( r
the minimum value of y = xx ]
t
,{
ti
.:
3
i
d
.i
8. e
Coo ftqfrqen* TiHTo,q
Tfl{r{s vft, f1x ) = r6sin x + 3cos x
' ol{lqtm r'(x)=.'.6.orx-3sinx
,!.rq {frthn-.r< wi f '(x)= 0, slcqt
.6.osx -3silrx =0=)tallx = l/-*x=T/.
/.!3 /o
wt<R f "(x )= -.6rin x - 3cos x
{fi x =y6 ,E{F f,,
w)
":tr I
iu
3cos
< 2a <-mftco .1, =
<i3, 1
u
-r, =.'r +sin 2.r for 0 < x <Ztt )
yN]{r.rs vfr f(x) = x+sin2x
vrqr' qErc, f '(^ )
=
I * 2cos 2x
,{?rdr {kfu"r <l s&eTrr{R q{I
w<Qu r
.t'
;i
J
)
?ir.' r i.-i:i
f)
--l2)
t -4sln 7r/ -/-1 -2J1<i0.',, : ,;,::*tlr. t
l:::::r ir::i:: ::.: =-r:,:jj-.-_:=.t
,ii
r
VJ sln
{s-<l( x =r/oAnro 6sinx+3cosx e<{frtTr{qEqr
.q< cqt, ntT*fr Sp, $q r< $,qy€ 0<x,<2n ffik6o
:
)
9. Fr{ftffi E"r"ttI,.j
.'. '-i =
4f; A,nw f(x) .r<
"r ftqrn qTfq q<( otfu${1afi
Co)
Efisfi
qfr6fi{ qte q<( Frfr&
t P%) = r% *,i,.,(+fi) = r% - J|/
' ", , i{:.''1,
, ,L ).:r i
lrrcm [" (*) = 2(.ostr x + cosx)
rrrt{ x-0. s"ta f
,'(rt)=
2(.u.1.,0+cos0)= 2(t +
{E(1( x=0 f+.nro qq*E {n?.rr.r< -fusn" Tfe €<(
l)=4>tl
:'
,(
l
I
i
i
:
!
i
ri
I
ii
I
J
E
i{
5
:l
T
EI
Eq'R3"t )e3 _f (*)= et + Zcosx + e-^ rfls.lrd1-1 Efr$:flr
[Examine the function f (*)=e. +2cosx+ e-., for
val ues]
sm !r{ r
10. Frflfw E:1'nn " Ce"e
)= 2xr -9xr + 12 -3 qti-RF< .{fr8qtq e<( FTFi6TFT fi.ftr oa"r
[Find the maximum and minimum values of the function
ofthefunction f(x)=xi-5xt+5x3-ll,,,'r ffi5pve
x)=5xt' +18x5 +l5x{ -1g q{irllFcqs qfrrTn e<( qfurh{rd
rtER iF-( r I Investigate for what values " of x,
+18x5 +l5xa *l0has the maxi
s.I
r(*): 2x3 - 9xr +tz-31 ufr )tqs,us
,
Nfrfu rrt(,H8<
'fR6flq, .qr( qfrt$q wi-Elutl ,, iEiro
{ ft)= x't - 5x{ + 5x
j
- I [Discuss the maximum arrci nrinimum
,' .. r ]
fl<.RE<
e< r I Discuss the maximurn and mini
function f(x)= x-' -3x' + 3x + I I
,i,;i J:
'.:,!:d..:ri:
+5 ,{l
o) cRXls.6r",.x
qnq r I Plpve that .l'(.r)=sin.u(l+cos,r.)' haS, a maximunt, r
'rrltrc
lor.
^
=%l
i
)blb
ffirya'i'*u,
cr f (x)= x3 -6xr il2x -3 e< ,ffr&{1q TfFrqfle
'/*,
t Show that f(x)=*l-o*'i ii-t
maximum nor a minimuml
,/7
>>/m,t;rs c< f (x )= x3 - 3x
3
+ 6x
,/
' nR [Show rhar f(x)= x:
maximum nor a minimum value]