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
Process for volume of revolution
Use correct formula depending on which axis is that of rotation.
Substitute in our equation for the graph. Square the equation and take pi out to the side. Use square brackets to evaluate limits and solve.
