Final Review Flashcards
derivative of f(x)/g(x)
[g(x)fā(x) - f(x)gā(x)]/(g(x)^2)
derivative sin(x)
cos(x)
derivative tan(x)
sec^2(x)
derivative cos(x)
-sin(x)
derivative sec(x)
sec(x)*tan(x)
derivative cot(x)
-csc(x)
integral of -csc(x)*cot(x)
csc(x)
integral of 1/sqrt(1-x^2)
arcsin(x)
integral of 1/1+x^2
arctan(x)
integral of 1/abs(x)*sqrt(x^2-1)
arcsec(x)
integral of b^x
b^x/ln(b)
integral of ln (x)
x * ln(x) - x
trig identity with cos and sin squared
sin^2 + cos^2 = 1
trig identity that equals sec^2
1 + tan^2
trig identity that equals csc^2
1+cot^2
MacLaurin for 1/1-x
x^n
MacLaurin for e^x
x^n/n!
MacLaurin for sin(x)
-1^n (x^(2n+1) / (2n+1)!)
MacLaurin for cos(x)
-1^n (x^2n / (2n+1)!)
MacLaurin for ln(1+x)
-1^(n+1) x^n/n
MacLaurin of arctan(x)
-1^n (x^(2n+1) / 2n+1)
MacLaurin of (1+x)^r
(r n) x^n
integral of -1/sqrt (1-x^2)
-1/sqrt (1-x^2)arccos(x)
integral of -1/1+x^2
arccot(x)
integral of -1/ abs(x)* sqrt(x^2-1)
arccsc(x)
integral of tan(x)
-ln |cos(x)|
integral of sec(x)
ln |sec(x)+tan(x)|
trig identity for sin^2(x)
1/2 - cos(2x)
formula for Taylor series
f^(n)(a) / n! * (x-a)^n
to convert polar to cartesian
x = r * cos(x) y = r * sin(x)
to convert cartesian to polar
r = sqrt ( x^2 + y^2 ) theta = arctan ( y/x ) r^2 = x^2 + y^2
