January 2014
Intermediate to advanced
144 pages
4h 2m
English
Content preview from Mathematical Formulas for Industrial and Mechanical Engineering
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G
L’Hopital’s rule:
lim
x!c
f ðxÞ
gðxÞ
5 lim
x!c
f
0
ðxÞ
g
0
ðxÞ
; if lim
x!c
f ðxÞ5 lim
x!c
gðxÞ5 0orN:
5.7 Indefinite Integral
Functions: f, g, u, v
Independent variables: x, t, ξ
Indefinite integral of a function:
ð
f ðxÞdx;
ð
gðxÞdx; ...
Derivative of a function:
y
0
ðxÞ; f
0
ðxÞ; F
0
ðxÞ; ...
Real constants: C, a, b, c, d, k
Natural numbers: m, n, i, j
G
ð
f ðxÞdx 5 FðxÞ1 C; if F
0
ðxÞ5 f ðxÞ
G
ð
f ðxÞdx
0
5 f ðxÞ
G
ð
kf ðxÞdx 5 k
ð
f ðxÞdx
G
ð
½f ðxÞ1 gðxÞdx 5
ð
f ðxÞdx 1
ð
gðxÞdx
G
ð
½f ðxÞ1 gðxÞdx 5
ð
f ðxÞdx 2
ð
gðxÞdx
G
ð
f ðaxÞdx 5
1
a
FðaxÞ1 C
G
ð
f ðax 1 bÞdx 5
1
a
Fðax 1 bÞ1 C
G
ð
f ðxÞ f
0
ðxÞdx 5
1
a
f
2
ðxÞ1 C
G
ð
f
0
ðxÞ
f ðxÞ
dx 5 lnjf ðxÞj1 C
73Calculus
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.