Exam 1 Flashcards
integral of 1/x
ln abs value x
integral e to the x
e to the x
integral sinx
-cosx
integral sec^2x
tanx
integral secxtanx
secx
integral secx
ln I secx + tanx I
integral tanx
ln I secx I
integral 1/(sq. root 1-x^2)
arcsinx (sin-1x)
integral b^x
b^x/lnb
integral cosx
sinx
integral csc^2x
-cotx
integral cscxcotx
-cscx
integral cscx
ln I cscx-cotx I
integral cotx
ln I sinx I
integral 1/x^2 +1
arctanx (tan-1x)
sin^2x + cos^2x
1
tan^2x +1 =
sec^2x
1 + cot^2x =
csc^2x
sin2x
2sinxcosx
cos2x
cos^2x - sin^2x
2cos^2x-1
sin^2x =
1/2 (1-cos2x)
cos^2x=
1/2(1+cos2x)
tan^2x=
(1-cos2x)/(1+cos2x)
volume of a sphere
v= 4/3 pi r^3
area of a pyramid or cone
v= 1/3 (area of base) height
volume of prism or cylinder
v= (area of base) height
cos (0)
1
cos(pi/6)
(sq root 3)/2
cos(pi/4)
(sq root 2)/2
cos(pi/3)
1/2
cos(pi/2)
0
cos pi
-1
sin(0)
0
sin(pi/6)
1/2
sin(pi/4)
(sq root 2)/2
sin(pi/3)
(sq root 3)/2
sin(pi/2)
1
sin(pi)
0
tan(0)
0
tan(pi/6)
(sq root 3)/3
tan(pi/4)
1
tan(pi/3)
sq root 3
tan(pi/2)
undefined
tan(pi)
0
graph y=x^2 - 2
parabola shifted down 2
graph y= (x-3)^2
parabola shifted to the right 3
trig integrals sincos
if sin power is odd use cos^2x= 1-sin^2x and make u=sinx
if cos power is odd use sin^2x= 1- cos^2x and make u=cosx
if they are both even use half angle identities
trig identities tansec
if sec is even, use sec^2x=1+tan^2x and make u=tanx
if tan is odd, use tan^2x=sec^2x -1 and make u=secx
trig sub
a2-x2 -> x=asin(theta)
a2+x2 -> x=atan(theta)
x2-a2 -> x=asec(theta)
integral of 1/(x^2+a^2)
1/a ⢠tan-1 (x/a) +C
comparison theorem
f(x)>g(x)
if f(x) is convergent then g(x) is convergent
if g(x) is divergent then f(x) is divergent
lim r^n
0 if -1
geometric series
E ar^n-1
geometric series sum
s=a/1-r and r<1, converges
diverges if r>or= 1
if lim an
doesnt exist or doesnt equal 0, divergent
arc length
L= integral of the sq. root (1+fâ(x)^2)
p-series
if p>1 convergent
if p<1 divergent
