Hyperbolics

Question 1

cosh x =

Answer 1

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

Question 2

sinh x =

Answer 2

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

Question 3

tanh x

Answer 3

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

Question 4

sinh x graph

Answer 4

cubic

Question 5

sinh x domain

Answer 5

all real values of x

Question 6

sinh x range

Answer 6

all real values of x

Question 7

cosh x graph

Answer 7

quadratic through (1,0)

Question 8

cosh x domain

Answer 8

all real values of x

Question 9

cosh x range

Answer 9

y>=1

Question 10

tanh x graph

Answer 10

asymtotes at x = 1 and x= -1 curves through (0,0)

Question 11

tanh x domain

Answer 11

all real values of x

Question 12

tanh x range

Answer 12

-1 <= y <= 1

Question 13

cosh^2 x - sinh^2 x =

Answer 13

1

Question 14

cos^2 x + sin^2 x =

Answer 14

1

Question 15

cosh 2x =

Answer 15

2cosh^2 x -1

Question 16

cos 2x =

Answer 16

2cos^2 x -1

Question 17

derivative of sinh x

Answer 17

cosh x

Question 18

derivative of cosh x

Answer 18

sinh x

Question 19

derivative of sin x

Answer 19

cos x

Question 20

derivative of cos x

Answer 20

• sin x

Question 21

maclaurin series of sinh and cosh

Answer 21

same for sin and cos

Question 22

why is the negative square root discarded when finding inverse hyerbolics

Answer 22

√(k^2 + 1) > k

Question 23

inverse sinh x

Answer 23

ln(x+√(x^2+1))

Question 24

inverse cosh x

Answer 24

ln(x+√(x^2-1))

x>= 1

Question 25

inverse tanh x

Answer 25

1/2ln((1+x)/(1-x))

|x|<1

Question 26

inverse sinh x graph

Answer 26

reflection of the cubic in y=x

Question 27

inverse cosh x graph

Answer 27

√x graph

Question 28

inverse tanhx graph

Answer 28

asymtotes at y = -1 and y = 1 and curves through 0

Question 29

why is it significant that arcsinh and arctanh are 1-to-1 but arccosh isn’t

Answer 29

arccosh will have two roots to the equation

Question 30

derivative of arcsinh x

Answer 30

1/ √(1+x^2)

Question 31

derivative of arccosh x

Answer 31

1/√(x^2 -1)

Question 32

derivative of arctanh x

Answer 32

1/ (1-x^2)

Question 33

integral of a 1/ √(a^2+x^2)

Answer 33

arcsinh(x/a) + c

Question 34

integral of 1/√(x^2 -a^2)

Answer 34

arccosh(x/a) + c

Question 35

integral pf 1/√(a^2 - x^2)

Answer 35

arcsin(x/a) + c