Trade Unions in Uganda Mostly by the Pdf Essay

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Systems of Units. Some Important Conversion Factors
The most important systems of units are shown in the table below. The mks system is also known as the International System of Units (abbreviated SI), and the abbreviations sec (instead of s), gm (instead of g), and nt (instead of N) are also used.

System of units

Length

Mass

Time

Force

cgs system

centimeter (cm)

gram (g)

second (s)

dyne

mks system

meter (m)

kilogram (kg)

second (s)

newton (nt)

Engineering system

foot (ft)

slug

second (s)

pound (lb)

1 inch (in.) ϭ 2.540000 cm

1 foot (ft) ϭ 12 in. ϭ 30.480000 cm

1 yard (yd) ϭ 3 ft ϭ 91.440000 cm

1 statute mile (mi) ϭ 5280 ft ϭ 1.609344 km

1 nautical mile ϭ 6080 ft ϭ
…show more content…
uvЈ uЈv Ϫ uvЈ u Ј
(ᎏ) ϭ ᎏᎏ v2 v du du dy
ᎏϭᎏ•ᎏ
dx dy dx

(Chain rule)

(x n)Ј ϭ nxn؊1
(e x)Ј ϭ e x
(e ax)Ј ϭ ae ax
(a x)Ј ϭ a x ln a
(sin x)Ј ϭ cos x
(cos x)Ј ϭ Ϫsin x
(tan x)Ј ϭ sec2 x
(cot x)Ј ϭ Ϫcsc2 x
(sinh x)Ј ϭ cosh x
(cosh x)Ј ϭ sinh x

n

͵ 1 dx ϭ ln ͉x͉ ϩ c x ͵ e dx ϭ 1 e ϩ c a ͵ sin x dx ϭ Ϫcos x ϩ c
͵ cos x dx ϭ sin x ϩ c
͵ tan x dx ϭ Ϫln ͉cos x͉ ϩ c
͵ cot x dx ϭ ln ͉sin x͉ ϩ c
͵ sec x dx ϭ ln ͉sec x ϩ tan x͉ ϩ c
͵ csc x dx ϭ ln ͉csc x Ϫ cot x͉ ϩ c
1
dx x ͵ ᎏ ϭ ᎏ arctan ᎏ ϩ c a x ϩa a ax

ax

2

2

x dx ͵ ᎏᎏ ϭ arcsin ᎏ ϩ c a ͙a ෆϪෆෆ
ෆ ෆx
2

2

x dx ͵ ᎏᎏ ϭ arcsinh ᎏ ϩ c a ͙x ෆෆෆ
ෆϩa
2

2

x dx ͵ ᎏᎏ ϭ arccosh ᎏ ϩ c a ͙x ෆෆෆ
ෆϪa
2

2

͵ sin x dx ϭ _ x Ϫ _ sin 2x ϩ c
͵ cos x dx ϭ _ x ϩ _ sin 2x ϩ c
͵ tan x dx ϭ tan x Ϫ x ϩ c
͵ cot x dx ϭ Ϫcot x Ϫ x ϩ c
͵ ln x dx ϭ x ln x Ϫ x ϩ c
͵ e sin bx dx
2

1
(ln x)Ј ϭ ᎏ x loga e
(loga x)Ј ϭ ᎏ x 1
2

1
4

2

1
2

1
4

2

2

1
(arcsin x)Ј ϭ ᎏᎏ
͙1ෆෆ2
ෆ Ϫ xෆ
1
(arccos x)Ј ϭ Ϫ ᎏᎏ
͙1ෆෆ2
ෆ Ϫ xෆ
1
(arctan x)Ј ϭ ᎏ
1 ϩ x2
1
(arccot x)Ј ϭ Ϫ ᎏ
1 ϩ x2

ax

ϭ

͵e

ax

eax

a2 ϩ b 2

(a sin bx Ϫ b cos bx) ϩ c

cos bx dx eax ϭ 2
(a cos bx ϩ b sin bx) ϩ c a ϩ b2

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ADVANCED
ENGINEERING
MATHEMATICS

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10

TH EDITION

ADVANCED
ENGINEERING
MATHEMATICS
ERWIN KREYSZIG
Professor of Mathematics
Ohio State University

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