Pure Flashcards
State the substitution used for an integral of the form a^2-x^2
let x = asinu
State the substitution used for an integral of the form a^2+x^2
let x = asinhu or let x = atanhu
State the substitution used for an integral of the form x^2-a^2
let x = acoshu or x=asecu
What is the form of the general equation used to model limacons, cardiods, eggs and dimples?
r = a(p+qcosθ) or r= a(p+qsinθ)
For what values of p and q is a graph a limacon?
p≥q
For what values of p and q is a graph a cardiod?
p=q
For what values of p and q is a graph an egg?
p≥2q
For what values of p and q is a graph a dimple?
q ≤ p ≤ 2q
For what values of θ are dimples concave?
θ=0
What is the relationship between the values of r and θ for the point of intersection between two polar curves?
The point of intersection of two polar curves has the same value of r and θ
To show that two lines lie in the same plane what must you show?
You must show that the two lines intersect and so they lie on the same plane
When an object has been displaced away from its equilibrium position what do we need to be careful with?
Choosing if it is a positive or a negative displacement
Explain how to find the line of intersection of two planes
- The position vector is a point that lies on a line which is contained by the two planes
- The direction vector is a vector perpendicular to both normal vectors of the two planes so use the cross product
When is matrix multiplication possible?
Two matrices can be multiplied if the number of columns in the left hand matrix are the same as the number of rows in the right hand matrix
When rotating about an axis by 180 degrees during volume of revolutions how does the formula change?
The Pi outside the integral changes to a Pi/2
