Applied algebra and calculus Flashcards
Acceleration of motion in a straight line =
a = f’’(t)=dv/dt=d^2x/dt^2
Velocity =
dx/dt
How to work out when a projectile hits ground
use y equation and solve t for y=0
How to work out magnitude of v in a plane =|v|
|v|=((dy/dt)^2+(dx/dt)^2)^1/2
Related rates of change question
Differentiate equations and use parametric differentiation to combine into one related rate equation.
Local minimum occurs when..
d^2y/dx^2>0
Local maximum occurs when..
d^2y/dx^2<0
Process for optimisation
Work out equation.
Differentiate equation.
Substitute in 0 for dy/dx at stationary points.
Differentiate equation again and state nature of the stationary point.
Area between functon and above x axis
Integrate with limits
Area between two functions, 1 segment
Integrate upper limit - lower limit with limits
Area between function all below x axis
= - integral of f(x) with limits
Area between two functions with 2 segments
Integral of upper limit - lower limit (limits)+ integral of new upper limit - new lower limit(new limits)
Finding the area with respect to the y axis process
Rearrange the formula so x is subject, then integrate f(y).
Volume of revolution equation about the x axis
Volume = §limitspiy^2dx
Volume of revolution about the y axis
Volume =§limits pix^2dy
