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urp:algebra [2021-11-08] nerf_herder |
urp:algebra [2021-12-19] nerf_herder [Functions] |
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S = n/2 (2a + (n − 1) d) | S = n/2 (2a + (n − 1) d) | ||
+ | Convergence of a power sequence: http://math.bu.edu/people/prakashb/Teaching/32LS10/Lectures/11-2.pdf | ||
====Factorial==== | ====Factorial==== | ||
n! = n * (n-1)! | n! = n * (n-1)! | ||
Line 70: | Line 71: | ||
Graphing an inverse: reflection of the graph about the line y=x | Graphing an inverse: reflection of the graph about the line y=x | ||
- | **horizontal and vertical asymptotes:** | + | **asymptotes** |
y = (quadratic1 of x) / (quadratic2 of x) | y = (quadratic1 of x) / (quadratic2 of x) | ||
* vertical asymptotes (VA) are when denominator goes to zero | * vertical asymptotes (VA) are when denominator goes to zero | ||
* horizontal asymptotes (HA) is when x goes to infinity, look at highest order of x in numerator and denominator: | * horizontal asymptotes (HA) is when x goes to infinity, look at highest order of x in numerator and denominator: | ||
* y = axⁿ / bxᵏ | * y = axⁿ / bxᵏ | ||
- | * if n > k : no HA | ||
* if n < k : HA = 0 | * if n < k : HA = 0 | ||
* if n = k : HA = a/b | * if n = k : HA = a/b | ||
+ | * if n > k : no HA | ||
+ | * if n = k+1 : oblique (diagonal) asymptote - approaches the line y = mx+b (from polynomial long division) | ||
+ | * if n > k+1 : no asymptote | ||
+ | |||
+ | look halfway down the page here: https://www.mathsisfun.com/algebra/rational-expression.html | ||
====Interest, half life, amortization==== | ====Interest, half life, amortization==== |