Calculus Final Exam Review

1
Calculus Final Exam Review

• By Bryant Nelson

2
Common Trigonometric Values
3
Special Trigonometric Limits
1
0
4
Differentiation Rules
Definition of a Derivative
f(x)
5
Differentiation Rules cont.
Product Rule
(fg) fg fg
Quotient Rule
(f/g) (fg - fg)/g2
Natural Log Rule
d/dx(ln(u)) (1/u)du/dx
Exponential Rules
d/dx(eu) (eu)du/dx

d/dx(bu) (bu) ln(b)du/dx
6
Differentiation Rules cont.
Trigonometric Rules
d/dx(sin(u))
(cos(u))du/dx
d/dx(cos(u))
(-sin(u))du/dx
d/dx(tan(u))
(sec2(u))du/dx
d/dx(cot(u))
(-csc2(u))du/dx
d/dx(sec(u))
(sec(u)tan(u))du/dx
d/dx(csc(u))
(-csc(u)cot(u))du/dx
7
Differentiation Rules cont.
Inverse Trigonometric Rules
d/dx(sin-1(u))
(1/(v1-u2))du/dx
d/dx(cos-1(u))
(-1/(v1-u2))du/dx
d/dx(tan-1(u))
(1/(1u2))du/dx
d/dx(cot-1(u))
(-1/(1u2))du/dx
d/dx(sec-1(u))
(1/(uvu2-1))du/dx
d/dx(csc -1(u))
(-1/(uvu2-1))du/dx
8
Integration Rules
Power Rules
?(undu) (un1)/(n1) C only while n ? -1
?(u-1du) ln(u) C
Exponential Rules
?(eudu) eu C
?(budu) bu/ln(b) - u C, b?1
Logarithmic Rule
?(ln(u)du) uln(u) - u C, ugt0
9
Integration Rules cont.
Trigonometric Rules
?(sin(u)du)
-cos(u) C
?(cos(u) du)
sin(u) C
?(tan(u) du)
-ln(cos(u)) C
?(cot(u) du)
ln(sin(u)) C
?(sec(u) du)
ln(sec(u) tan(u)) C
?(csc(u) du)
ln(csc(u) cot(u)) C
10
Integration Rules cont.
Trigonometric Rules cont.
?(sec2(u) du)
tan(u) C
?(csc2(u) du)
-cot(u) C
?(sec(u)tan(u) du)
sec(u) C
?(csc(u)cot(u) du)
-csc(u) C
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Summation Formulas
n
(n(n1))/2
(n(n1)(2n1))/6
(n2(n1)2)/4