Flashcards
2021-09-18
What is the trapezium rule for estimating $T_n$, the integral of a function $f(x)$ between $a$ and $b$ and using $n$ strips??
$$ T_n \frac{\Delta X}{2}\left( f(x_0) + 2f(x_1) + … + 2f(x_{n-1}) + f(x_n) \right) $$
where
$$ \Delta X = \frac{b - a}{n} $$
What is magical about $$\frac{1}{2n}\left(1 + 2b + 2b^2 + 2b^3 + … + 2b^{n-1} + b^n\right)$$??
The middle bit is the sum of a geometric sequence.
Why do you have to be careful taking the reciprocal of both sides of an inequality??
It can flip the inequality.
How can you simplify $$\frac{b + 1}{b - 1}$$??
Use algebraic long division.
If you get a quotient $q$ and remainder $r$ when doing the algebraic long division $$\frac{f(x)}{g(x)}$$ what is the overall result of the division??
$$ q + \frac{r}{g(x)} $$
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date: 2021-09-18 18:22
summary: what properties does this function that behaves like an exponential have?
tags:
- '@?public'
- '@?mat'
- '@?notes'
- '@?maths'
title: MAT - Paper 2014 - Q3