Final Exam Flashcards
1
Q
d/dx sinx
A
cosx
2
Q
d/dx cosx
A
-sinx
3
Q
d/dx tanx
A
sec^2x
4
Q
d/dx cotx
A
-csc^2x
5
Q
d/dx secx
A
tanxsecx
6
Q
d/dx cscx
A
-cscxcotx
7
Q
d/dx arcsinx
A
1/sqrt(1-x^2)
8
Q
d/dx arccosx
A
-1/sqrt(1-x^2)
9
Q
d/dx arctanx
A
1/(1+x^2)
10
Q
d/dx arccotx
A
-1/(1+x^2)
11
Q
d/dx arcsecx
A
1/|x|sqrt(x^2-1)
12
Q
d/dx arccscx
A
-1/|x|sqrt(x^2-1)
13
Q
d/dx sinhx
A
coshx
14
Q
d/dx coshx
A
sinhx
15
Q
d/dx tanhx
A
sech^2x
16
Q
d/dx cothx
A
-csch^2x
17
Q
d/dx sechx
A
-sechxtanhx
18
Q
d/dx cschx
A
-cschxcothx
19
Q
d/dx arcsinhx
A
1/sqrt(x^2+1)
20
Q
d/dx arccoshx
A
1/sqrt(x^2-1)
21
Q
d/dx arctanhx
A
1/(1-x^2)
22
Q
d/dx arccothx
A
1/(1-x^2)
23
Q
d/dx arcsechx
A
-1/xsqrt(1-x^2)
24
Q
d/dx arccschx
A
-1/|x|sqrt(1-x^2)
25
Arc Length Formula
ds = sqrt(1+(dy/dx)^2)dx
26
Simpsons Rule Formula
Δx/3*(y0+4y1+2y2+4y3+4y4+2y5+4yn-1+yn)
27
Disk Method around x-axis Formula
V = π∫(y^2)dx
28
Disk Method around y-axis Formula
V = π∫(x^2)dx
29
Shell Method around a Vertical Line
V = 2π∫xf(x)dx
30
Shell Method around a Horizontal Line
V = 2π∫yf(y)dx
31
Surface Integral around x-axis
S = 2π∫ysqrt(1+y'^2)dx
32
Surface Integral around y-axis
S = 2π∫xsqrt(1+x'^2)dx
33
Geometric Series Convergence Formula
r*(1/(1-r))
34
Taylor Series Coefficient Formula
f^(n)(x)/n!
