Calculus Concepts For Ch. 1 And Section 2.1

Front 1

common types of behavior associated with the nonexistence of a limit

Back 1

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

Front 2

common types of behavior associated with the nonexistence of a limit

Back 2

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

Front 3

1st special limit

Back 3

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

Front 4

2nd special limit

Back 4

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

Front 5

3rd special limit

Back 5

lim (1+x)^(1/x) =e
x->0

*e is a mathematical constant*

Front 6

definition of continuity
(use when asked to discuss continuity)

Back 6

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

Front 7

discontinuities
example:
(x+1)/[(x+1)(x-2)]
where is this function discontinuous? What kind of discontinuities are these?

Back 7

at x= -1, there is a discontinuity. removable, (hole)

at x=2 there is a discontinuity. nonremovable, asymptotic

Front 8

derivative of a function
(long version)

Back 8

f'(x)= lim [f(x+h)-f(x)]/h
x->h

Front 9

notation for derivatives

Back 9

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