Further Pure 3

Question 0

Integral of cosech^2(x)

Answer 0

-coth(x) + c

Question 1

Integral of sech^2(x)

Answer 1

tanh(x) + c

Question 2

Integral of sech(x)tanh(x)

Answer 2

-sech(x) + c

Question 3

Integral of cosech(x)coth(x)

Answer 3

-cosech(x) + c

Question 4

Define “cosh(x)” in terms of e

Answer 4

cosh(x) = 1/2([e^x] + [e^-x])

Question 5

Define “sinh(x)” in terms of e

Answer 5

sinh(x) = 1/2([e^x] - [e^-x])

Question 6

Define “tanh(x)” in terms of e

Answer 6

tanh(x) =

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

Question 7

What is arsinh(x) in terms of x?

Answer 7

arsinh(x) = ln[x + sqrt(x^2+1)]

Question 8

What is arcosh(x) in terms of x?

Answer 8

arcosh(x) = ln[x +/- sqrt(x^2-1)]

Condition: x >or= 1

Question 9

Define artanh(x) in terms of x

Answer 9

artanh(x) = 1/2[ln(1+x / 1-x)]

Conditions |x| < 1