Calculus Formula Sheet PDF

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Calculus BC Formula Sheet with all the formulas you need....

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AP CALCULUS BC Stuff you MUST Know Cold

l’Hopital’s Rule ∞ , f ( a) 0 = If or = ∞ g ( a) 0

f (x) f '( x ) then lim = lim x → a g (x ) x → a g '( x )

Properties of Log and Ln 1. ln 1 = 0 2. ln e a = a 3.e

ln x

n 4. ln x = n ln x

=x

5. ln ( ab ) = ln a + ln b 6.ln (

a

b

“PLUS A CONSTANT” The Fundamental Theorem of Calculus b

∫ f (x )dx = F (b ) − F (a )

) = ln a − ln b

a

Average Rate of Change (slope of the secant line) If the points (a, f(a)) and (b, f(b)) are on the graph of f(x) the average rate of change of f(x) on the interval [a,b] is

f (b)− f (a ) b− a

where F '(x ) = f (x )

Differentiation Rules Chain Rule

d du [ f ( u) ] = f '( u) dx dx Product Rule

d dv du ( uv ) = u + v dx dx dx

2

nd

d dx

Fundamental Theorem of Calculus g (x )

∫

Average Value

Quotient Rule

Definition of Derivative (slope of the tangent line)  f ( x + h) − f ( x )  f '(x ) = lim   h→ 0 h  

Derivatives d n x ) = nxn −1 ( dx d ( sin x) = cosx dx d ( cos x) = −sin x dx d ( tan x) = sec2 x dx d ( cot x) = − csc 2 x dx d ( sec x ) = tanx sec x dx d ( csc x ) = − cot x csc x dx d ( ln u ) = 1 du dx u d u ( e ) = eu du dx 1 d log a x) = ( dx x ln a d u ( a ) = ax (ln a ) du dx

d u   = dx  v 

v

du dv −u dx dx 2 v

Mean Value & Rolle’s Theorem If the function f(x) is continuous on [a, b] and the first derivative exists on the interval (a, b), then there exists a number x = c on (a, b) such that f '(c ) =

f (b ) − f (a ) b −a

f (x )dx = f ( g (x )) ⋅ g '( x )

#

If the function f(x) is continuous on [a, b] and the first derivative exist on the interval (a, b), then there exists a number x = c on (a, b) such that

f (c) =

1 b−a

dy dx

= 0 or undefined. dy goes (-,0,+) or local minimum: dx d2y >0 (-,und,+) or dx 2 dy local maximum: goes (+,0,-) or dx d2y...