NtME
PAUrus
STUDENT NO :
CODE ;
RUNDU
22/078681
MAT - 36 21
CAMpus
ASSTGMMENT 2
Olaui HASTRU
CALCuluS 1 AsSICGNMENT 2
Moue he ind wtr th lgerithn
Cancel
b) c1
alr-) tan 2
in
im
6in()rn (-)
he (os
)
comPert and ubstitre
Lainy th propotes of grita1 to Jimple'y te Aiml
3 ele
=1
(e3)-ak
lin (1)*-)
{1+)*-)
(1r2)-1
T0
Dihrantiatirg numoatar
(er).2
l(er)'(T-) (lz21)
Diteaertiatingpingorrator
3T)I-!
(31)T +T- (T-)(+ B1)3
Fim
-3)
-.
e
0x e
im ( l
Sinee, e
as
X= 0 sO
thepand.
upulation
wt
be
bafsk
no bewin
stabte
There
the Then
P=o
0=p(6
toteter
=0.05
hen
IEB
)
Ta
staba
pupulotins
art
(p--0-0Sp
0 oo)=
=-0.05p
p0 -
Goo
500P PC=C)
0.05p)
P)(0cKD-PE
-P)
0-04P
C)
Stoable
pupuletion
gives
a)
23
31
gie) = 2+ (x -5)
k)= 3l-5)2
=>(3-5)=o
hu 5
a cnitc! nunber ot
Jeunetim
g(a)=2t (a-s
pen hoterval (e, 6) cenlaining 5
and
Jus
g5)) ga) for r«5
so thu
functon 9) =2t(a-s) dos not
Yalue at
=5
heut a ocl eotrem
we
hawt
the euerage
wedth ot
3ter
u
be
Depth wiu et te gutte
ww be
h cros Sectinal atae
Sinte +cos t
=fl coset cos (o) -l
= (cose)-) (cos (o) +)
0=(ecose) -) (cos(o tI)
/t=
= 60
yz0
&= 60
guter
ne area
wu zeo LTu
win cTy te
/s
cast ot miinun arca
maznun ameurt et water.
3k
hterating wth regpect to a ouer (a, )
lue
a)
J a lalde
Yalue ct flccs fun ction o! x e hutervol
(-5, -2) = -3
(-2, -i) z2
0,
-z
2--2-re-t)
cos xto (os)- sin ' ( )
tran'form
to
Usiny the doubu -ana
by ugune
2J3cosY
sec')
se,
=Jsos)nin) Sey)
d.
Sec-)
then dul =
dz
se&)
a)d
at tan')
2see' (u0 dua)
B+tantut
(uc)duo)
= let ue) = tan (u)u, duty = Sec'
du)= du)
by uing uQ) and duce)
dutt)
w-t:t.
aretan
ute)s r c t n
) tC
=) Simpayng
uarctn
tan (t3) te
)_Jsin(a) t sin)
2S)n x t2 sina csa
daxSin x
du
VI-(u -i)
= Vzu
Sina
tc
|+sinx
dx
1t Sin (3)
sinxdr
Seca tan x dx
= tant
Sect +1