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How to convince students of the integral identity $\int_0^af(x)dx=\int_0^af(a-x)dx$?
2 votes

In $\int_0^af(x)\,dx$, the inputs to $f$ begin at $0$ and progress to $a$. In $\int_0^af(a-x)\,dx$, the inputs to $f$ begin at $a$ and progress to $0$. So when considering Riemann sums with uniform-...

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Factoring quadratics where the coefficient on the $x^2$ term does not equal 1
13 votes

Quadratic Formula (deterministic---no guess and check about it) The QF yields that $-{\frac13}$ and $5$ are roots. So $$3x^2-14x-5=c\left(x+\frac13\right)(x-5)$$ Comparing leading coefficients, $c$ ...

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Regarding AMATYC's draft position statement on the academic preparation of mathematics faculty at two-year colleges
Accepted answer
7 votes

After writing an email, I received a response from Ernie Danforth, the NE regional vice president of AMATYC which answer my question. Keep in mind these are GUIDELINES, they are not hard and fast ...

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