Calc Study Cards

Front 1

even function

Back 1

f(x) = f(-x) symmetric with respect to y axis.

Front 2

odd function

Back 2

f(-x) = -f(x)
symmetric with respect to origin

Front 3

Rational Function

Back 3

ratio of two polynomials P(x) / Q (x)

Front 4

f(x) + c

Back 4

shift vertically

Front 5

f(x) - c

Back 5

shift downward

Front 6

f(x-c)

Back 6

shift c units right

Front 7

f(x+c)

Back 7

shift c units left

Front 8

cf(x)

Back 8

stretch graph vertically by factor c

Front 9

1/c f(x)

Back 9

compress graph vertically by factor c

Front 10

f(x/c)

Back 10

stretch graph horizontally by factor c

Front 11

-f(x)

Back 11

reflect graph about x-axis

Front 12

f(-x)

Back 12

reflect graph about y axis

Front 13

Limit 1 definition

Back 13

the limit of f(x), as x approaches a, equals L

Front 14

lim sin x / x as x > 0

Back 14

1

Front 15

lim pie / x as x >0

Back 15

does not exist

Front 16

Precise definition of a limit

Back 16

for every e>0 there is a corresponding d>0 such that if 0<I x-a I < d then I f(x) - LI < e

Front 17

Lim cf(x)

Back 17

c lim f(x)

Front 18

lim (f(x) ^n

Back 18

(lim f(x) ^n

Front 19

lim c

Back 19

c

Front 20

lim x as x >a

Back 20

a

Front 21

lim x^n as x > a

Back 21

a^n

Front 22

lim sqaure root x as x approaches a

Back 22

square root of a

Front 23

lim cos phi as phi >0

Back 23

0

Front 24

limit sin phi as phi > 0

Back 24

0

Front 25

lim sin as phi >a

Back 25

sin a

Front 26

lim cos as phi > a

Back 26

cos a

Front 27

limit sin (1/x) as x > 0

Back 27

does not exist

Front 28

limit sin x / x

Back 28

1

Front 29

limit sin phi / phi

Back 29

1

Front 30

continuity definition of limit

Back 30

lim f(x) as x >a = f(a)

Front 31

if f and g are continuous at a and c is a constant then the following functions are also continuous

Back 31

f +g f-g fg f/g cf

Front 32

functions continuous at every number in their domains

Back 32

polynomials, rational functions, root functions, trigonometric functions

Front 33

theorem 7

Back 33

if f is continuous at b and lim g (x) - b then lim f(g(x) = f(b)

Front 34

theorem 8

Back 34

if g is continuous at a and f is continuous at g(a) then the composite function f o g given by (fog) (x) = f(g(x) is continuous at a

Front 35

intermediate value theorem

Back 35

f is continuous on closed interval (a,b) and N is any number between f(a) and f(b) there there exits a number c in (a,b) such that f(c) = N

Front 36

limit x / x -a

Back 36

positive infinity from right negative from left

Front 37

limit tan x as x > pie/2

Back 37

infinity from left positive from right negative

Front 38

limit x2-1 / x2+1

Back 38

1 limit at infinity will approach fraction of x coefficients

Front 39

limit 1/x^n as x > infinity

Back 39

0

Front 40

limit sin 1/x as x > infinity

Back 40

0

Front 41

Infinite Limits Precise Definition

Back 41

let f be a function defined on some open interval that contains the number a, then lim f(x) x>a = postive infinity for every postive number M there is a postive number d such that if 0< Ix -aI<e then f(x)>M

Front 42

lim 1/ sin x as x approaches pie/2

Back 42

from left postive infinity from right negative infinity

Front 43

derivative of ln x

Back 43

1/x

Front 44

derivative csc x

Back 44

-csc x cotx

Front 45

f' sec x

Back 45

sec x tanx

Front 46

f' tan x

Back 46

sec^2x

Front 47

f' cot x

Back 47

-csc2x