Hsc - Calc Ii Test 1 - Some Concepts

Front 1

derive ln(x)

Back 1

1/tdt

so integral of 1/t dt = ln(x)

Front 2

ln 1 =

Back 2

0

Front 3

ln(ab)=

Back 3

ln a + ln b

Front 4

ln (a ^n)

Back 4

n ln(a)

Front 5

ln(a/b)

Back 5

ln(a)-ln(b)

Front 6

e is?

Back 6

the base for natural log

Front 7

ln e =

Back 7

1
also, integral 1/t dt from 1 to e

Front 8

derive nat log:
ln(u)

Back 8

1/u*(du/dx)

only include the du dx if the u is a chain rule and not just an x

Front 9

d/dx of ln abs(u)

Back 9

u'/u

Front 10

integral 1/x

Back 10

ln abs (x)

Front 11

integrate (1/u)

Back 11

ln abs(u) + c

Front 12

integral sin u

Back 12

-cos u +c

Front 13

integral cos u

Back 13

sin u + c

Front 14

integral tan u

Back 14

ln abs(sin u ) + c

Front 15

inverse of the natural log is the

Back 15

natural exponential function,
f^-1(x)=e^x

Front 16

e^a*e^b=

Back 16

e^a+b

Front 17

e^a/e^b

Back 17

e^a-b

Front 18

d/dx e^u

Back 18

e^u*(du/dx)

only include the du/dx if the u is a chain rule, if not the e^x derives to itself.

Front 19

integral of e^u du

Back 19

e^u+c

Front 20

a^x=

Back 20

(ln a)*a^x

Front 21

loga(x)=

log base a of x

Back 21

1/(ln a)*(ln x)

Front 22

d/dx (a^u)=

Back 22

(ln a)*a^u *du/dx

Front 23

d/dx (log a u)

derivative, log base a of u

Back 23

1/((ln a)u) * du/dx

only additional multiply for du/dx if its a chain rule

Front 24

d/dx u^n

Back 24

n*u^(n-1) * du/dx

only additional multiply for du/dx if its a chain rule

Front 25

inverse trig functions: input/output ?

Back 25

input ratio and output angle

Front 26

accoridn gto the formula sheet, the what are the formulas of the functions not given :
arcsin ->
arctan ->
arcsec ->

Back 26

arccos
arccot
arccsc

all now include a negative u' on top.

Front 27

exponential growth and decay model

Back 27

y=Ce^kt

Front 28

d/dx ln(u)

Back 28

u'/u

Front 29

ln(0)

Back 29

undefined

Front 30

e^1

Back 30

e

Front 31

cos(0)

Back 31

1

Front 32

sin(0)

Back 32

0

Front 33

e^0

Back 33

1