Calculus

Question 1

Describe the integration by parts method

Answer 1

Question 2

State the derivative of sin(x)

Answer 2

cos(x)

Question 3

State the derivative of cos(x)

Answer 3

-sin(x)

Question 4

State the derivative of tan(x)

Answer 4

-sec²(x)

Question 5

State the requirement for an ODE Pdx + Qdy = 0 to be an exact differential

Answer 5

If ∂P/∂y = ∂Q/∂x, the ODE is an exact differential

Question 6

State the derivative of sec(x)

Answer 6

sec(x)tan(x)

Question 7

Describe how to solve an exact differential of the form

Pdx + Qdy = 0

Answer 7

Let P = ∂F/∂x and Q = ∂F/∂y and solve for F.

Note that F = constant

Question 8

Describe the absolute error in a taylor series expansion

Answer 8

|f(x,x₀) - p(x,x₀)|