Ap Calc

Front 1

lim (1-cosx) =
x->0 x

Back 1

0

Front 2

lim (sinx) =
x->0 x

Back 2

1

Front 3

y=cosx

Back 3

R: [-1,1]
D: (-∞,∞)

y-intercept: (0,1)

x-intercepts: multiples of (π/2)

Front 4

y=sinx

Back 4

R: [-1,1]
D: (-∞,∞)

y-intercept: (0,0)

x-intercepts: multiples of (π)

Front 5

unit circle

Back 5

(1,0) = 0 or 2π
(0,1) = (π/2)
(-1,0) = π
(0,-1) = (3π/2)

Front 6

Squeeze Theorem

Back 6

If h(x) ≤ f(x) ≤ g(x) for all x in an open interval containing c, except possibly c itself, and if the

lim h(x) = L = lim g(x)
x->c x->c

then the lim f(x) exists and is equal to L.
x->c

Front 7

Existence of a Limit

Back 7

lim f(x) = L = lim
x->c¯ x->c+

Front 8

Definition of Continuity

Back 8

1. f(c) is defined
2. lim f(x) = exists if (- and +)
x->c
3. f(c) = lim f(x)
x->c

Front 9

Intermediate Value Theorem

Back 9

f must be continuous on a closed interval [a, b] and K is a # b/n f(a) and f(b), then there is at least one # c in [a, b] such that f(c) = k.


*used for zeroes

Front 10

Continuity of a Composite Function

Back 10

If g is continuous at c and f is continuous at g(c) then (f • g) (x) is continuous at x = c.

Front 11

d/dx [tanx] =

Back 11

(secx)^2

Front 12

d/dx [secx] =

Back 12

sextanx

Front 13

d/dx [cotx] =

Back 13

- (cscx)^2

Front 14

d/dx [cscx] =

Back 14

- cscxcotx