AP Calc Flashcards
1
Q
sin^2 x + cos^2 x
A
1
2
Q
sin 2x
A
2sinxcosx
3
Q
d/dx tanx
A
sec^2 x
4
Q
d/dx cotx
A
-csc^2 x
5
Q
d/dx secx
A
secxtanx
6
Q
d/dx cscx
A
-cscxcotx
7
Q
d/dx a^x
A
a^x lna
8
Q
d/dx loga x
A
1/xlna
9
Q
d/dx arcsinx
A
1/sqrt(1-x^2)
10
Q
d/dx arccosx
A
-1/sqrt(1-x^2)
11
Q
d/dx arctanx
A
1/1+x^2
12
Q
d/dx arccotx
A
-1/1+x^2
13
Q
d/dx arcsecx
A
1/|x|sqrt(x^2-1)
14
Q
d/dx arccscx
A
-1/|x|sqrt(x^2-1)
15
Q
Derivative (limit definition)
A
lim h->0 f(x+h)-f(x) / h
16
Q
Arc length (Cartesian)
A
Int a->b sqrt(1+(dy/dx)^2)
17
Q
Speed
A
Sqrt(x’^2+y’^2)
18
Q
Distance traveled
A
Int a->b sqrt(x’^2+y’^2)
19
Q
Arc length (parametric)
A
Int a->b sqrt((x’)^2 + (y’)^2)
20
Q
Trapezoidal approximation
A
1/2(w(b1+b2) + w(b2+b3) …)
21
Q
Fraction decomposition
A
Ky(L-y) = L / 1+Ce^-Lkt
22
Q
Washer method
A
pi * Int R(x)^2 - r(x)^2
23
Q
Shell method
A
2pi * Int r(x)h(x)
24
Q
Polar area
A
1/2 Int r^2
