All Formulas Except Chp 5

Question 0

|x|

Answer 0

{x if x>=0 and -x if<0

Question 1

e

Answer 1

lim n>∞(1+(1/n))^n

Question 2

f’(x)- definition

Answer 2

f’(x)= limn-∞ (f(x*h)-f(x))/h

Question 3

f’(a)- definition

Answer 3

lim x-a (f(x)-f(a))/(x-a)

Question 4

Average rate of change of f(x) on [a,b]

Answer 4

( f(b)-f(a)) / (b-a)

Question 5

Rolle’s Theorem

Answer 5

If f is continuous on [a,b] and differentiable on (a,b) and if f(a)=f(b), then there is at least one number c on (a,b) such that f’(c)=0.

Question 6

Mean Value Theorem

Answer 6

If f is continuous on [a,b] and differentiable on (a,b), then there exists a number c on (a,b) such that f’(c)=(f(b)-(f(a))/(b-a)

Question 7

Intermediate Value Theorem

Answer 7

If f is continuous on [a,b] and k is any number between f(a) and f(b), then there is at least one number c between a and b such that f(c)=k.

Question 8

sin2x

Answer 8

2sinxcosx

Question 9

cos2x

Answer 9

cos^2x-sin^2x
1-2sin^2x
2cos^2x-1

Question 10

cos^2x

Answer 10

(1+cos2x)/2

Question 11

sin^2x

Answer 11

(1-cos^2x)/2

Question 12

d/dx[c]

Answer 12

0

Question 13

d/dx[uv]

Answer 13

uv’*vu’

Question 14

d/dx[f(g(x))]

Answer 14

f’(g(x))*g’(x)

Question 15

d/dx[sinu]

Answer 15

cosu(du/dx)

Question 16

d/dx[tanu]

Answer 16

sec^2u (du/dx)

Question 17

d/dx[secu]

Answer 17

secutanu(du/dx)

Question 18

d/dx [lnu]

Answer 18

(1/u)*(du/dx)

Question 19

d/dx[e^u]

Answer 19

e^u (du/dx)

Question 20

d/dx [arcsinu]

Answer 20

1/(√1-u^2) *du/dx

Question 21

d/dx [arctanu]

Answer 21

1/(1+u^2) * du/dx

Question 22

d/dx [arcsecu]

Answer 22

1/(|u|√u^2-1) * du/dx

Question 23

(F^-1)(a)

Answer 23

1/f’(f^-1(a))

Question 24

∫cosu

Answer 24

sinu+ C

Question 25

∫sec^2udu

Answer 25

tanu+C

Question 26

∫secutanu du

Answer 26

secu+ C

Question 27

∫ 1/u du

Answer 27

ln|u| + C

Question 28

d/dx [x^n]

Answer 28

nx^n-1

Question 29

d/dx [u/v]

Answer 29

(vu'-uv')/v^2

Question 30

d/dx [cosu]

Answer 30

-sinu+C

Question 31

d/dx[cotu]

Answer 31

-csc^2u (du/dx)

Question 32

d/dx [cscu]

Answer 32

-cscucotu (du/dx)

Question 33

d/dx [logau]

Answer 33

1/ulna (du/dx)

Question 34

d/dx[a^u]

Answer 34

a^u*lna*(du/dx)

Question 35

∫sinu du

Answer 35

-cosu + C

Question 36

∫csc^2u du

Answer 36

-cotu+C

Question 37

∫cscucotu du

Answer 37

-cscu + C

Question 38

∫tanu du

Answer 38

-ln|cosu| + C

Question 39

∫secu du

Answer 39

ln|secu+tanu| +C

Question 40

∫e^u du

Answer 40

e^u +C

Question 41

∫du/(u√u^2-a^2)

Answer 41

1/a arcsec (|u|/a) +C

Question 42

∫du/ (√a^2-u^2)

Answer 42

arcsin(u/a) +C

Question 43

∫cotu du

Answer 43

ln|sinu| + C

Question 44

∫cscu du

Answer 44

-ln|cscu+cotu| + C

Question 45

∫a^u du

Answer 45

a^u/lna +C

Question 46

∫du/(u^2+a^2)

Answer 46

(1/a) arctan(u/a) + C