General stuff

Question 1

Horizontal tangent =

Answer 1

dy/dt = 0 ( dx/dt ≠ 0 )

Question 2

e^-lnx =

Answer 2

e^-lnx =1/x

Question 3

Is it

tanh²x + sech²x = 1

OR

tanh²x - sech²x = 1

Answer 3

tanh²x + sech²x = 1

Question 4

What id the formula for a linear approximation?

Answer 4

y - f(x₁) = f’(x₁)(x - x₁)

y - y₁ = m(x-x₁)

Question 5

What is newtons method?

Answer 5

x_n+1 = x_n - f(x_n) / f’(x_n)

eg.

x₂ = x₁ - f(x₁) / f’(x₁)

Question 6

What are problems with Newtons method?

Answer 6

If initial guess is bad, you may get further from the answer. If graph is symmetrical you will be in an inifinte loop.