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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 (1-cos 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)(x-2)]
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'