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17 Cards in this Set
 Front
 Back
lim(x→a) [f(x) + g(x)] =

lim(x→a)f(x) + lim(x→a)g(x)


lim(x→a) [c f(x)] =

c lim(x→a) f(x)


lim(x→a) [f(x) ÷ g(x)] =

lim(x→a)f(x) ÷ lim(x→a)g(x)
if lim(x→a)g(x) ≠ 0 

lim(x→a) [f(x)]n =

[ lim(x→a) f(x) ]^n
where n is a positive integer 

The Squeeze Theorem

If f(x) ≤ g(x) ≤ h(x)
when x is near a (except possibly at a) and lim(x→a) f(x) = lim(x→a) h(x) = L then lim(x→a) h(x) = L 

(derivative of a constant function)
d/dx (c) = 
0


d/dx (x) =

1


(power rule)
d/dx (x^n) = 
nx^(n1)


(the constant multiple rule)
d/dx [cf(x)] = 
c d/dx f(x)


(the sum rule)
d/dx [f(x) + g(x)] = 
d/dx f(x) + d/dx g(x)


(the difference rule)
d/dx [f(x)  g(x)] = 
d/dx f(x)  d/dx g(x)


(the product rule)
d/dx [f(x)g(x)] = 
f(x) d/dx[ g(x)] + g(x) d/dx[ f(x)]


(the quotient rule)
d/dx [f(x) / g(x)] = 
( g(x) d/dx[f(x)]  f(x) d/dx[g(x)] )
÷ [g(x)]^2 

(the chain rule)
F'(x) = 
f '(g(x)) • g'(x)
Leibniz notiation: dy/dx = (dy/du) (du/dx) 

(the chain rule & power rule)
d/dx [g(x)]^n = 
n[g(x)]^(n1) • g'(x)
Alternatively: d/dx [u^n] = nu^(n1) du/dx 

Formal Definition of a Derivative
The tangent line to the curve y=f(x) at the pointP(a, f(a)) is the line through P with the slope... 
m = lim(x→a) [(f(x)  f(a)] / [x  a]


Formal Definition of a Derivative Using H
The tangent line to the curve y=f(x) at the pointP(a, f(a)) with (h = x  a) & (x = a + h) is the line through P with the slope... 
m = lim(h→0) [(f(a+h)  f(a)] / h
