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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'