Calc 2 Final

tan(x)+c

sin(x)

-cos(x)

asin(o)

atan(o)

asec(o)

-sin(x)

ln(|x|)+c

sec²(x)

tan(x)sec(x)

arcsin(u/a)+c

1/a arctan(u/a)+c

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

1/x

Alternative series test

1.limit approaches 0, 2. n>(n+1), f(n)>0

Ratio test (L<1)

Converges absolutely

Ratio test (L>1)

Diverges

Ratio test (L=1)

Inconclusive

P series test

if P>1, converges

Taylor series

Cn = f^(n)(a)/n!

Maclaurin series

f^(n)(0)/n! (x^n)

Area of cardioid

½ [(outside)²-(inside)²do

arc length of cardioid

[sqrt(r²)+(r’)²do

number of petals in rose curve

if N is even then 2N, if N is odd then N

polar coordinates rotate around the x axsis

sin(o)

polar coordinates rotate around the y axsis

cos(o)

Horizontal cardioid

Cos(o)

vertical cardioid

Sin(o)

a/b=1

Heart(touch pole)

a/b>1

Heart point moves left by a-b(more rounded)

a/b<1

Inner circle (inner circle touches b-a)