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9 Cards in this Set
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common types of behavior associated with the nonexistence of a limit

1. f(x) approaches a different number from the right side of c than it approaches from the left side of c.
2. f(x) increases or decreases without bound as x approaches c. 3. f(x) oscillates between 2 fixed values as x approaches c 

common types of behavior associated with the nonexistence of a limit

1. f(x) approaches a different number from the right side of c than it approaches from the left side of c.
2. f(x) increases or decreases without bound as x approaches c. 3. f(x) oscillates between 2 fixed values as x approaches c 

1st special limit

lim (sin x)/x =1
x>0 

2nd special limit

lim (1cos x)/x =0
x>0 

3rd special limit

lim (1+x)^(1/x) =e
x>0 *e is a mathematical constant* 

definition of continuity
(use when asked to discuss continuity) 
a function f is continuous at c if the following 3 conditions are met:
1. f(c) is defined 2. lim f(x) exists x>c 3. lim f(x) = f(c) x>c 

discontinuities
example: (x+1)/[(x+1)(x2)] where is this function discontinuous? What kind of discontinuities are these? 
at x= 1, there is a discontinuity. removable, (hole)
at x=2 there is a discontinuity. nonremovable, asymptotic 

derivative of a function
(long version) 
f'(x)= lim [f(x+h)f(x)]/h
x>h 

notation for derivatives

f'(x), dy/dx, y'
