Bits and bobs Flashcards
What is an odd function?
When -f(x) = f(-x)
What is an even function?
When f(x) = f(-x)
What are the limits if a function is rotated about the x axis?
X- Values
When the function is rotated about the y-axis, what is the subject of the function?
X=…. (f(y))
What does a row of zero’s indicate?
The equation is redundant. There are an infinite number of soliutions
What happens if a row becomes 000:5?
The system of equations is inconsistent. There is no solution to the system of equations
What is an ill-conditioned system of equations?
A small change in the equations leads to a significant change in the solutions.
If x=y^3/4 what does y=?
y=x^4/3
f’(y) =?
1/dx/dy
If y=sin^(-1)x/a what does dy/dx equal?
(a^2-x^2)^1/2
If y=cos^(-1)x/a what does dy/dx equal?
(a^2-x^2)^1/2
If y=tan^(-1)x/a what does dy/dx equal?
a^2+x^2
If the equation for a circle is x2 + y2 + 2gx + 2fy + c = 0, what is the centre?
(-g,-f)
If the equation representing a circle is (x – a)2 + (y – b)2 = r2 what is the centre?
a,b
What is the equation for the radius of a circle?
(g^2 +f^2 -c)^1/2
What does dy/dx equal when differentiating parametric equations?
dy/dt x 1/dx/dt
What is the formula to work out the second derivative of parametric equations?
d/dt of (dy/dx) x dt/dx
What is the formula for integration in parts?
INT(fg’)=fg - INT(f’g)
What is the domain and range for sin^-1x ?
Domain, between -90 and +90
Range, between -1 and 1
What is the domain and range for cos^-1x?
Domain, between 0 and 180
Range, between -1 and 1
What is the domain and range for tan^-1 x?
Domain, between -90 and +90
Range, between -infinity and positive infinity.
What is the order of a differential equation?
The order of the highest derivative involved. dy/dx = 1st d^2y/dx^2 = 2nd
What is the degree of a differential equation?
The power of the highest derivative involved.
What is the formula for an arithmetic sequence?
Un= a+d(n-1)
What is the formula for a geometric sequence?
Un=ar^(n-1)
What is the formula for an arithmetic series?
Sn = n/2(2a + (n-1)d)
What is the formula for an arithmetic series if you know the last term?
Sn = n/2 (a+L)
What is the formula for a geometric series?
Sn = a(1-r^n)/(1-r)
What is the formula for a geometric series when r > 1
Sn = a(r^n -1)/(r-1)
