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AP Calculus BC SUMNOCO Limits Curve Sketching and Analysis More Derivatives

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AP Calculus BC SUMNOCO Limits Curve Sketching and Analysis More Derivatives
Limits
Notation for:
Limit from the left of () as  → 
AP Calculus BC SUMNOCO
Curve Sketching and Analysis
Critical Points:
Global Min:
Limit from the right of () as  → 
More Derivatives
Where  is a function of 
and a is a constant

(  ) =



Global Max:



Definition of Continuity
A function is continuous at the point
 =  if and only if:
Point of Inflection:
1.
Derivatives





Definition of Derivative
d
 f ( x)  
dx
2.
3.



Situations in which limits fail to
exist:


Alternate Form of Def. of Derivative
d
 f ( x)  at x  c
dx




Situations in which derivatives fail
to exist:

Chain Rule
d
[ f (u )] 
dx




Point-Slope Form:
ln 1 =
Product Rule
d
(uv) 
dx


ln  =
Intermediate Value Theorem


Quotient Rule
d u
 
dx  v 
Where  and  are functions of 
Solution to / = 
(sin ) =
(cos ) =
(tan ) =
(cot ) =
(sec ) =
(csc ) =
(ln ) =
(  ) =
(−1 ) =
(sin−1 ) =
(cos −1 ) =
(tan−1 ) =
(  ) =
(log  ) =
Extreme Value Theorem
The Mean Value Theorem
(derivatives)
Rolle’s Theorem
Distance, Velocity, and
Acceleration
() is the position function,
 x(t ), y (t )  is the position in
parametric
velocity =
Parametric Equations
dy

dx
d2y

dx 2
acceleration =
Arc length =
velocity vector =
The Fundamental Theorem of
Calculus
acceleration vector =
Polar Curves
4 conversions
speed (rectangular and parametric) =
Area =
2nd FTC
d g ( x)
f (t )dt 
dx a
displacement =
Slope =
distance (rectangular and parametric)
=
Taylor Series
Area Under The Curve
(Trapezoids)
average velocity =
Maclaurin Series
l'Hôpital's Rule (Bernoulli’s Rule)
Sum of infinite geometric
Mean Value Theorem for Integrals
(Average Value)
ex 
Euler’s Method
Solids of Revolution and Friends
Disk Method
cos x 
sin x 
Washer Method
1

1 x
General volume equation
Integration by Parts
ln( x  1) 
Arc Length (rectangular)
Logistics
dP

dt
Series Tests/Error Bound
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