Hyperbolics Flashcards
1
Q
cosh x =
A
1/2(e^x +e^-x)
2
Q
sinh x =
A
1/2(e^x - e^-x)
3
Q
tanh x
A
(e^x - e^-x)/(e^x +e^-x)
4
Q
sinh x graph
A
cubic
5
Q
sinh x domain
A
all real values of x
6
Q
sinh x range
A
all real values of x
7
Q
cosh x graph
A
quadratic through (1,0)
8
Q
cosh x domain
A
all real values of x
9
Q
cosh x range
A
y>=1
10
Q
tanh x graph
A
asymtotes at x = 1 and x= -1 curves through (0,0)
11
Q
tanh x domain
A
all real values of x
12
Q
tanh x range
A
-1 <= y <= 1
13
Q
cosh^2 x - sinh^2 x =
A
1
14
Q
cos^2 x + sin^2 x =
A
1
15
Q
cosh 2x =
A
2cosh^2 x -1
16
Q
cos 2x =
A
2cos^2 x -1
17
Q
derivative of sinh x
A
cosh x
18
Q
derivative of cosh x
A
sinh x
19
Q
derivative of sin x
A
cos x
20
Q
derivative of cos x
A
- sin x
21
Q
maclaurin series of sinh and cosh
A
same for sin and cos
22
Q
why is the negative square root discarded when finding inverse hyerbolics
A
√(k^2 + 1) > k
23
Q
inverse sinh x
A
ln(x+√(x^2+1))
24
Q
inverse cosh x
A
ln(x+√(x^2-1))
x>= 1
25
inverse tanh x
1/2ln((1+x)/(1-x))
| |x|<1
26
inverse sinh x graph
reflection of the cubic in y=x
27
inverse cosh x graph
√x graph
28
inverse tanhx graph
asymtotes at y = -1 and y = 1 and curves through 0
29
why is it significant that arcsinh and arctanh are 1-to-1 but arccosh isn't
arccosh will have two roots to the equation
30
derivative of arcsinh x
1/ √(1+x^2)
31
derivative of arccosh x
1/√(x^2 -1)
32
derivative of arctanh x
1/ (1-x^2)
33
integral of a 1/ √(a^2+x^2)
arcsinh(x/a) + c
34
integral of 1/√(x^2 -a^2)
arccosh(x/a) + c
35
integral pf 1/√(a^2 - x^2)
arcsin(x/a) + c
