Further Algebra Flashcards
(14 cards)
What is the sum of 1, r=1 to n
n
What is the sum of r from r=1 to n
1/2(n)(n+1)
What is the method of differences?
Seeing when the summation cancels at certain points and deducing only some things are left.
What is the maclaurin series
F(x) = f(0) + f ‘ (0) + f’’(0)/2! +…+ fr(0)/r!
What is the maclaurin series for (1+x)^n
= 1 + nx + (n(n-1)/2! )x^2 +…+ n(n-1)…(n-(r-1))/r!
Binomial expansion |x| < 1
Maclaurin series for e^x
1 + x + 1/2! X^2 + 1/3! X^3 +…+ 1/r! X^r
XER
Maclaurin series for ln(1+x)
X - 1/2 x^2 + 1/3 x^3 - 1/4 x^4 +….
Valid for -1<x=<1
Maclaurin series for sinx and cosx
Sinx= x - 1/3! X^3 + 1/5! X^5 +1/7! X^7 +…..
Cosx= 1 - 1/2! X^2 +1/4! X^4 +1/6!X^6 +…..
What is lhopitals rule
When lim x~c f(x)/g(x) has f(x)=g(x)=0, +/- infinity
And then we use f ’ (x)/ g ‘ (x) to see what the function tend to
What are the steps to draw a reciprocal graph
1) find vertical asymptotes
2) find x and y intercepts
3) find horizontal asymptotes by dividing the fraction by x^n
When is there an oblique asymptote and how do you find it
When the order of polynomial is higher on the numerator, if its higher by 2 powers then its a quadratic oblique asymptote.
Do algebraic division on the function and see what it tends to, this is the equation of the asymptote.
What is the equation of a parabola
y^2 = 4ax
What is the equation of an elipse
X^2/a^2 + y^2/ b^2 = 1
What is the equation of a hyperbola
X^2/ a^2 - y^2/b^2 = 1
Where when x,y tends to infinity, y= +/- b/a is an asymptote
