2 - 6 hyperbolic functions

Question 1

sinhx

Answer 1

( e^x - e^-x ) /2

Question 2

cosh x

Answer 2

( e^x + e^-x ) /2

Question 3

tanhx

Answer 3

( e^x - e^-x ) / ( e^x + e^-x )
= (e^2x - 1) / (e^2x + 1)

Question 4

graph of sinhx cosh x tanhx

Answer 4

sinhx - liek tan or an S but the otehr way round ( points up and down)
cosh x like a bowl U
tanhx S - sinhx on its side ∫

Question 5

domain and range for sinhx coshx tanhx

Answer 5

sinhx - x and f(x) all R
coshx - x all R, f(x) >= 1
tanhx - x all R, -1 < f(x) <1

Question 6

graph of inverse sinhx coshx tanhx

Answer 6

arcsinhx - S curve ∫
coshx - starts at (1,0) then goes up and plateause
arctahx - same as sinhx S on its side

Question 7

hyperbolic idenities

Answer 7

cosh^2 - sinh^2 = 1
1- tanh^2 - sech^2
coth^2 - 1 = cosech^2

Question 8

how to get from trig identities to hyperbolic

Answer 8

replce all trig with hyperbolic trig
where there is a product of 2 sines put a negative in front

Question 9

differentiating hyperbolics

Answer 9

sinhx > coshx
coshx > sinhx

Question 10

intergrating hyperbolics

Answer 10

∫sinhx = coshx + c
∫coshx = sinhc
∫tanh x = ln cosh x