&
one-to-one :
Cakes
never
honzontal live Est
Force
.
,
vee versa
logs
((xy)
strictly increasing (f(x) > 0 for all x)
or
Or
4
laws of
same value
on
switch
In (xr)
:
my m(y)
(nx +
=
rInx
=
b
my
exponents lams :
bx + y
b" by
*
=Y
TiticalRInerpason para
inverses
S
D &
inverses
m
res
(ab)
Y
ab"
=
constant base
leading
Coeffiorets
c
,
by
variable base , c
.
.
is
0
For base
degreen
↳ DNE
in
=
Mx
=
b
3
=
In b
:
&
V
Xlnb
e
known
forgun
&
sinx
&
cosx =
&/dx
.
>
x-
(s(x =
secx =
2x
Tanx-sec
dx
Cer [x
-
n -
cS(X cos e
(b
-
Seca
e
-
a
.
secs
setzy
dif
.
logb
x <
I
in
x
3
=
E
cosh2X-Sinhx
sinh(x +
=
-
c
x
Gorg
de
cost
y)
&di
+
ToL
impor
notes :
,
-
dxtan-x
-
dcot"
e
n
hyperboires
a/dx
x =
-
x
subtraction form
i
*
coshx
=
guosrent ,5
2
*
=
-
product :
-
dax Cox= ina
A
&
& Tannx
&x
=
=
- cschcoty
.
& tann" x
-10th -x
=
Fx2
tanhx & 10th <
dx
c
to
L
smh +
myperbol
x
=
cosh" x =
Tann"x
=
m(x + x
)xel
In (x +)
[In()
-1
x =1
Xc
I
Imit-0 0
,
Idtuz- Hareham
e
& arcsint
=
1
<
S(x xdx
Ssextanx
=
=
cosx + C
=
-
y
=
=
Sexte
Stanxdx I/Secx)
=
X(>
,
=
e
arcsecht
-
m(csex) + C
=
o
A
Csc2q
1)Standa
si+ (x)
siysx
cosyy
+C
-
y
e
uz
=
=
/Edu
-
I
1
sy
-x2
>
-
-
>
=
=
Sexsmny
dx
coshy
Y
=
kxl +
In/Secx) + C
y
y
=
0
sty
3
y
·
=
=
- In(ul + c
In (cosx /+ C
In
sinh" x
sinn-x
1
=,
x2
-
f(o(xdx
.
age
* +2090
1
Both +
n formulas
-8
i so I
Dann IX/
.
1
c
-
double
dX
Lax
e
x
·fsmn
Tra
1
,
limit =
C
=
Sechx--Sechxtanx
hyperboles
C
0-0
:
mis e
*
Secxtanx
=
Sechlothx--csch
&(ax inv
.
c
didysecx
i
MDNE
0
0
exponential
schx
t
&
@
:
I
-C
:
-fo e
&
Sinux
Sech"X
=
-
q
=
1 - tanhx
=
,
d
1
cosh
=
xtyC coshxcoshy simhxsinhing
d
dx
cosh(X)
sinhxcoshy + coshxsinhy
=
- -
.
:
- Sink
Inb
Mb
at
p
*
I
=
.
b YInb
↳
=
.
mb"
/
e
x
I
3
·
=
sanzy
x
sub
=
et
Simh(x)
=
uy X
Sin
=
3 x q2y
-
ey
-
=
2
ey - e y = 2x22
ey
⑱
+ - 2x
ey
1g) isE I Signi ↓
i ne
upperbole routrires
y
known
in (1 +i
sinh(x)
-sinx*
&
O
.
2 =
cosx
=
&
-
constant
exlub
>
sinh- (x) = m(x +
1)
In b
is
-Y 3
(n(( + x) 'x
e=
Y
eX
=
-
SaYax-
rlub
b
s
↳
In lesa
=
-
its
=
e
*
Y
proof :
>
f(x)"" Fi e
n
+x9 log
of logbx af it
denormotor
=
*)
exp
ynb
e
sin
.
=
change of base : Logox
by highest pur
durde
va r
,
degree denim
>
0
=
bg() 39(
,
-
&b
-
f(x)"
exp
insatione varexp
degree num-degreedenam
L=
(b)
exp :
.
eXlnb
<
b
(bY)Y i bYY
b
=
L = valuo of
16
b
>C
x-
degree num degreedemon
it
=
=
nx
=
ey
In
ey
~
1
=
2xey
0
2xey
qx2
167
+
-
=
=
y
=
-
2X
-
-
/
x
=
=
(n(x + x1)