Calculus I

Question 1

even function

Answer 1

f(-x) = f(x)

mirrors across y axis

Question 2

odd function

Answer 2

f(-x) = -f(x)

mirrors across origin

Question 3

to stretch a graph vertically or horizontally by C:

Answer 3

vertically = Cf(x)
horizontally = f(x/C)

Question 4

compress a graph vertically or horizontally by C:

Answer 4

vertically = (1/C)(f(x)
horizontally = f(Cx)

Question 5

reflect graph across x or y axis:

Answer 5

across x axis = -f(x)

across y axis = f(-x)

Question 6

trig values for 30°

Answer 6

30° = π/6
sin(π/6) = 1/2
cos(π/6) = √3/2
tan(π/6) = √3/3

Question 7

trig values for 60°

Answer 7

60° = π/3
sin(π/3) = √3/2
cos(π/3) = 1/2
tan(π/3) = √3

Question 8

trig values for 45°

Answer 8

45° = π/4
sin(π/3) = √2/2
cos(π/3) = √2/2
tan(π/3) = 1

Question 9

trig values for 90° and 180°

Answer 9

90° = π/2
sin(π/3) = 1
cos(π/3) = 0
tan(π/3) = DNE

180° = π
sin(π/3) = 0
cos(π/3) = 1
tan(π/3) = 0

Question 10

1 + (tanx)^2 =

Answer 10

(secx)^2

Question 11

1 + (cotx)^2 =

Answer 11

cscx^2

Question 12

addition formula for cos(A+B):

Answer 12

cosAcosB - sinAsinB

Question 13

addition formula for sin(A+B)

Answer 13

sinAcosB + cosAsinB

Question 14

double angle formula cos2x =

Answer 14

cosx^2 - sinx^2

Question 15

double angle formula sin2x =

Answer 15

2sinxcosx

Question 16

half angle formula cos(x)^2 =

Answer 16

(1 + cos2x)/2

Question 17

half angle formula sin(x)^2 =

Answer 17

(1 - cos2x)/2

Question 18

law of cosines

Answer 18

c^2 = a^2 + b^2 -2abcosC

Question 19

arccosx + arccos(-x) =

Answer 19

π

Question 20

arcsinx + arccosx =

Answer 20

π/2

Question 21

exponential growth function

Answer 21

y = y(0)*e^(kx)

Question 22

how to tell if a function is 1:1

Answer 22

horizontal line test

Question 23

ln(1/x) =

Answer 23

-lnx

Question 24

a^log(base a)x =

Answer 24

x

Question 25

x^n

Answer 25

e^(nlnx)

Question 26

change of base formula for log/ln

Answer 26

log(base a)x = lnx/lna

Question 27

ranges for inverse sin and cosine

Answer 27

sine range is -π/2 to π/2
cosine range is 0 to π

Question 28

lim sinx/x =

x->0

Answer 28

1

Question 29

derivative of lnu

Answer 29

(1/u)*(du/dx)

Question 30

derivative of a^u

a is a constant and u is a fx

Answer 30

a^u = (a^u)*lna(du/dx)

Question 31

derivative of log(base a)u

Answer 31

log(base a)u = 1/(ulna)*(du/dx)

Question 32

derivative of x^n

Answer 32

e^(nlnx)

use product chain rule to solve

Question 33

derivative of arcsinx

Answer 33

Question 34

derivative of arctanx

Answer 34

Question 35

derivative of arcsecx

Answer 35

arcsecx’ =

Question 36

derivatives of arccosu, arccotu, and arccscu

Answer 36

arccosu’ = - arcsinu

arccotu’ = - arctanu

arccscu’ = - arcsecu

Question 37

mean value theorem

Answer 37

f’(c) = (f(b) - f(a))/b-a = f’(c)

or f’(c) = slope m

Question 38

derivative of tanx

Answer 38

sec^2(x)

Question 39

derivative of secx

Answer 39

secxtanx

Question 40

derivative of cotx

Answer 40

-csc^2(x)

Question 41

derivative of cscx

Answer 41

-cscxcotx