Unit 1
fix
=
Linear
f (f (t)
((x)
-
f(a) + f((a)(X
=
=
((x)
im
0ima
= max
o
:
Ifixiaf(x) a
(aY )" = logax
+
,
a)
1
ef(x)
=
+
c
↓ & Concave
,
iif-1EX ?
Sinh (Sinh"x)
EX
Sinkx : in(x
iif.
=
+
X
Sinh" (Sinhx)
,
-x2
+
1)
Cosh"x
S
Cosh(coshx)
=
X
iif
=
Sin"()
=
x
D : <1 , a)
:
X
iif-1EX1
cosh" (coshx)
X
iif
Cos" (cosx)
=
X
iif
cosh" (x) = (n(x +
xz
0
XI
cosxsinx
xmlogax -im log i
X
Sinnix
=
iif XfR
infexig(x-fix
-x2",
--
X>
x(0
-
tanh(tanh" x )
=
.
tanctanix) = X iif
X Eith
Sech"(x) =
a
logax
logax
x
=
X0
,
harhL
:
logax xina
en(aY)
=
2
*
Sinh =
cosh
tann :
DORE , f(x inc
:
:
cosh2
+ c
Coth2
,
in D
,
-
Sinho
tank" (tanhx)
x
csch
:
1
,
cosh2
·
=
.
Ix 11
Sec" (Secx) = X iif
x [0.
Sinh(x + y)
,
(coshx + Sinhx)" = Coshux +
cosh(x + y) ,
=
>
tankx
i
:
Sec(secx) = X iif
=-
1
-
iif
Zin (i
:
d th,
&c
=
cosh(2x)
) u2n
,
:
tanh(x + y) :
It tanhxtanhy
m = 1
i
+
S
Jaxn
Sinhnx
:
)Ax
:
x
=
1
.
;
tank
1
;
Sech
m
=
e
i
m =
1
CS
=
Acaxtbl
Alcax
Ji
Anlax
J Acx
a
:
=
Syne dx
x ve
I
:
b2
Adx
Asdy
-
Md2
f(x)
Mass : e
:
:
nAxx
sel : v :
zunexd: mux
d
ninA
~: 2
+ (b2 - dz)
=
-
Li =
g(x)dx
Mx =
*
Unit 5
x
-
-may
S2πyH cydy
+
=
ydext
t
Y
(x : + 1
-
xim
(f(xi + 11
+
-
f (xi12
e (f(x g(x))dx
My
-
x
-
N :
.
=
n'
=
(Acxidx
2
A :
myy
eSP(XdX
Ne =
=
+
+
Y
Unit
?
arctanx
No
qx
A S T
.
=
X
lif
.
Say
(f(x) ex,
+
( f(x) g(x1)dx
x
e
=
an = c
=
.
alman
=
:
+ bn
.
X
.
,
.
=
+
Costo
COS20 :
&
+
=
f(x)
:
-
Sax =
1
-
Yi + 1)
:
<ti + Xt
,
Yi +
(ti
,
vi)dt)
Comp :
Dn
-cotcsc
J(fc)"f'(x)dx
=
lan/conv = An
COS (A + B))
1 : CSC2-cot2
COSACOSB :
[(COS (A-B)
x2
-
=
acoso
;
B T:
↑
DNE o r #O
& Brian
,
-
.
X = asinQ
a
+
x2
+
COS(A + B)
=
a seco
X = atan O
;
j (n1f(x)
=
a2
:
atano ; X = a seco
bal
for
E,
a
Mid
Kb
:M
Trap : In & Rn , in :
=X = b
(n
=
+
** (f(xal 2 f(x
+
Lim Comp Test
.
.
.
1+
+
f(Xn)
= f(xi 1)4XRn = f(xi)4x
-
,
Estaba
Sn =
=even
* f(x)
X =
+
P f(x , ) + 2 f(x2) +
+
f(x)
:
-as
(Xi -1 + xi)
.
,
Ixr :
Sinx
Sexet
Ssecritan
ICS-cot
Isectan
lati
Isin
| x1 n
conv
,
/cos
/sec
R= n
sin
:
Jac
In/sec + tanl
:
Stan
Ink-cot)
:
:
:
Scot
sec
Scot
Inse
:
:
-esc
conv
=
dimdii
·
In Sin
S
DIV
-
RT = O : Farall x
.
/conv
=
.
=
&
Sinn con
1 : 20 , 01
(x *
ia
for
conv ( =
R
:
an :
In
an conv
P
p-ser :
,
conv
.
i
,
ifpc
(a
1
=
an
Jaxu sin"(
tan
:
(n(x +
:
x2 + ar
(
IX-c1 < RE
Taylor :
conv.
n =o
fux-
Power : 1-bx
=
n :
-
1
,
i'x nX
09(bx11
=
-
1 , 1)
X
(n (1
-
x) =
-
n .,
M
In (1 + x)
=
anconu.lifan conv
danbnc
.
P
:=
harm
.
Ser
bx
=
n =
09)
-
bx ,
In (a-bx1) = n =
v
cosx :
-
xn + 1
n
.,
1)
ex =
no
Sinx :
not
,
=T-Ten
.
-R
< 1
,
.
1
:
(Cos (A-B)
Ex1ba
x:
an conve
.,
def
cont . +, & +on (1 a)
Conv
Ian
tanza :
SinAsinB =
(
,
cost
I : Sech-tan2
If "(x11[K
g(x)dy
(xn + andx
ccschdx
:
cs
=-
=
+
2n + 1
=
dx
+ Sin (A + B)
IE+ 1
S2πf(x)((x)
+
: (Sin(A-B)
*
/2nX((X)
e
SinAcosB
a2
+ (fxidx
*
1 = cos2 + Sin2
+
a
(ti + 1
S
Sinc :
-
d cot
+
n)x
-
o , con
baso , br = dec
G
r
(f'(x((2dx
1 +
A
-
A C T
1
Geo-s
arm
& Test : f
+
*
X = 0
r
Div-Test :
F((u q(x)dx c)
-
y =
im1
=
limbn
T(t) = T + cek
+ P(x)y
·
=
:
v
n)(Inx)" dx
-
=
g(xidx i
r
Stac
X(Inx)
((x2 andx
f
A =
:
X(x2 + a2 ,
secta
Cotm
;
n : 2
tanse/sechdx
J(inx(2dx
9
Scott sch
n : 2
Sinxo (cod
-
fexdx = limi
:
Y axis :
:
:
Costsin(sind
-
XEIR
if
Unit 4
X-axis
:
Isecdx
Sin20 = 2 SinCos
Stamsech
Sinn
n = 1
[ (1 + cos2X)
Jcsxdx
Ssin"cosudy
=
cos2x
x2
sec
tanhx + tanhy
tanh2 + Sech? : 1
* <x
-
cosho = 1
XC0
,
o
Sink"
Sec(x) & X-1
Judu an-Judu
IxK
=stance
o
X)0 dec
.
f(x) inc . , tanho
,
-
=
Real , al , f(x) inc
DER , REC-1 1) ,
:
Sinn2 = 1
·
,
.
iif
= x
tanix secran
; Due
exina
=
-e
Sin
tan" (tanx)
XEIR
,
=
,
exe" DER
=
X
=
Jax in1g(xi)
:
a
log(a*)
,
-
E(1-cos2X)
(sinxdx
1)
:
a
Sin2 :
(cosxdx
iif
x
Unit 3
:
cost :
in
:
,
=
R : [0 , 8)
Coscos"x)
cos
Mlogax loga
:
cschx
& sin"x cosinx) : x
as
:
<1
a
-
=
ma : In a
(fixef(dx
c
X
=
Sin' (Sinx) = x
a se
1 & concave
,
Sin(Sirix)
a)
-
x2 = x ,
ma
,
-
1 + ((xipdx
-
:
=
.
max ma a
=
at
cothx
Unit 2
:
not
tanxi
axN,
2
x , x
E